Displaying similar documents to “Operator Connes-amenability of completely bounded multiplier Banach algebras”

Operator Figà-Talamanca-Herz algebras

Volker Runde (2003)

Studia Mathematica

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Let G be a locally compact group. We use the canonical operator space structure on the spaces L p ( G ) for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues O A p ( G ) of the classical Figà-Talamanca-Herz algebras A p ( G ) . If p ∈ (1,∞) is arbitrary, then A p ( G ) O A p ( G ) and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that O A p ( G ) is a completely contractive Banach algebra for each p ∈ (1,∞), and that O A q ( G ) O A p ( G ) completely contractively...

C*-algebras have a quantitative version of Pełczyński's property (V)

Hana Krulišová (2017)

Czechoslovak Mathematical Journal

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A Banach space X has Pełczyński’s property (V) if for every Banach space Y every unconditionally converging operator T : X Y is weakly compact. H. Pfitzner proved that C * -algebras have Pełczyński’s property (V). In the preprint (Krulišová, (2015)) the author explores possible quantifications of the property (V) and shows that C ( K ) spaces for a compact Hausdorff space K enjoy a quantitative version of the property (V). In this paper we generalize this result by quantifying Pfitzner’s theorem. Moreover,...

On the H-property and rotundity of Cesàro direct sums of Banach spaces

Saard Youyen, Suthep Suantai (2008)

Banach Center Publications

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In this paper, we define the direct sum ( i = 1 n X i ) c e s p of Banach spaces X₁,X₂,..., and Xₙ and consider it equipped with the Cesàro p-norm when 1 ≤ p < ∞. We show that ( i = 1 n X i ) c e s p has the H-property if and only if each X i has the H-property, and ( i = 1 n X i ) c e s p has the Schur property if and only if each X i has the Schur property. Moreover, we also show that ( i = 1 n X i ) c e s p is rotund if and only if each X i is rotund.

On the Aronszajn property for integral equations in Banach space

Stanisław Szufla (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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For the integral equation (1) below we prove the existence on an interval J = [ 0 , a ] of a solution x with values in a Banach space E , belonging to the class L p ( J , E ) , p > 1 . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.

Sequentially Right Banach spaces of order p

Mahdi Dehghani, Mohammad B. Dehghani, Mohammad S. Moshtaghioun (2020)

Commentationes Mathematicae Universitatis Carolinae

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We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order p , and those defined by the dual property, the sequentially Right * Banach spaces of order p for 1 p . These classes of Banach spaces are characterized by the notions of L p -limited sets in the corresponding dual space and R p * subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space X and a reflexive Banach...

Pisier's inequality revisited

Tuomas Hytönen, Assaf Naor (2013)

Studia Mathematica

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Given a Banach space X, for n ∈ ℕ and p ∈ (1,∞) we investigate the smallest constant ∈ (0,∞) for which every n-tuple of functions f₁,...,fₙ: -1,1ⁿ → X satisfies - 1 , 1 | | j = 1 n j f j ( ε ) | | p d μ ( ε ) p - 1 , 1 - 1 , 1 | | j = 1 n δ j Δ f j ( ε ) | | p d μ ( ε ) d μ ( δ ) , where μ is the uniform probability measure on the discrete hypercube -1,1ⁿ, and j j = 1 n and Δ = j = 1 n j are the hypercube partial derivatives and the hypercube Laplacian, respectively. Denoting this constant by p ( X ) , we show that p ( X ) k = 1 n 1 / k for every Banach space (X,||·||). This extends the classical Pisier inequality, which corresponds to the special...

Δ -weak character amenability of certain Banach algebras

Hamid Sadeghi (2019)

Archivum Mathematicum

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In this paper we investigate Δ -weak character amenability of certain Banach algebras such as projective tensor product A ^ B and Lau product A × θ B , where A and B are two arbitrary Banach algebras and θ Δ ( B ) , the character space of B . We also investigate Δ -weak character amenability of abstract Segal algebras and module extension Banach algebras.

Limited p -converging operators and relation with some geometric properties of Banach spaces

Mohammad B. Dehghani, Seyed M. Moshtaghioun (2021)

Commentationes Mathematicae Universitatis Carolinae

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By using the concepts of limited p -converging operators between two Banach spaces X and Y , L p -sets and L p -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as * -Dunford–Pettis property of order p and Pelczyński’s property of order p , 1 p < .

-sums and the Banach space / c

Christina Brech, Piotr Koszmider (2014)

Fundamenta Mathematicae

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This paper is concerned with the isomorphic structure of the Banach space / c and how it depends on combinatorial tools whose existence is consistent with but not provable from the usual axioms of ZFC. Our main global result is that it is consistent that / c does not have an orthogonal -decomposition, that is, it is not of the form ( X ) for any Banach space X. The main local result is that it is consistent that ( c ( ) ) does not embed isomorphically into / c , where is the cardinality of the continuum,...

On (Co)homology of triangular Banach algebras

Mohammad Sal Moslehian (2005)

Banach Center Publications

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Suppose that A and B are unital Banach algebras with units 1 A and 1 B , respectively, M is a unital Banach A,B-module, = A M 0 B is the triangular Banach algebra, X is a unital -bimodule, X A A = 1 A X 1 A , X B B = 1 B X 1 B , X A B = 1 A X 1 B and X B A = 1 B X 1 A . Applying two nice long exact sequences related to A, B, , X, X A A , X B B , X A B and X B A we establish some results on (co)homology of triangular Banach algebras.

On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space

Artur Michalak (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function f : [ 0 , 1 ] m X is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function f : [ 0 , 1 ] m X with respect to any norming subset there exists a separately increasing function g : [ 0 , 1 ] m such that the sets of...

Reflexivity and approximate fixed points

Eva Matoušková, Simeon Reich (2003)

Studia Mathematica

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A Banach space X is reflexive if and only if every bounded sequence xₙ in X contains a norm attaining subsequence. This means that it contains a subsequence x n k for which s u p f S X * l i m s u p k f ( x n k ) is attained at some f in the dual unit sphere S X * . A Banach space X is not reflexive if and only if it contains a normalized sequence xₙ with the property that for every f S X * , there exists g S X * such that l i m s u p n f ( x ) < l i m i n f n g ( x ) . Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded...

Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi (2019)

Mathematica Bohemica

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The generalized notion of weak amenability, namely ( ϕ , ψ ) -weak amenability, where ϕ , ψ are continuous homomorphisms on a Banach algebra 𝒜 , was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the ( ϕ , ψ ) -weak amenability on the measure algebra M ( G ) , the group algebra L 1 ( G ) and the Segal algebra S 1 ( G ) , where G is a locally compact group, are studied. As a typical example, the ( ϕ , ψ ) -weak amenability of a special semigroup algebra is shown as well.

On some properties of generalized Marcinkiewicz spaces

Evgeniy Pustylnik (2001)

Studia Mathematica

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We give a full solution of the following problems concerning the spaces M φ ( X ) : (i) to what extent two functions φ and ψ should be different in order to ensure that M φ ( X ) M ψ ( X ) for any nontrivial Banach couple X⃗; (ii) when an embedding M φ ( X ) M ψ ( X ) can (or cannot) be dense; (iii) which Banach space can be regarded as an M φ ( X ) -space for some (unknown beforehand) Banach couple X⃗.

Non-regularity for Banach function algebras

J. Feinstein, D. Somerset (2000)

Studia Mathematica

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Let A be a unital Banach function algebra with character space Φ A . For x Φ A , let M x and J x be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of J x is connected, and that if x does not belong to the Shilov boundary of A then the set y Φ A : M x J y has an infinite connected subset. Various related results are given.

The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu (2017)

Commentationes Mathematicae Universitatis Carolinae

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ϵ Y have the w G P property, when X and Y have the w G P property.

A theorem of Gel'fand-Mazur type

Hung Le Pham (2009)

Studia Mathematica

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Denote by any set of cardinality continuum. It is proved that a Banach algebra A with the property that for every collection a α : α A there exist α ≠ β ∈ such that a α a β A is isomorphic to i = 1 r ( [ X ] / X d i [ X ] ) E , where d , . . . , d r , and E is either X [ X ] / X d [ X ] for some d₀ ∈ ℕ or a 1-dimensional i = 1 r [ X ] / X d i [ X ] -bimodule with trivial right module action. In particular, ℂ is the unique non-zero prime Banach algebra satisfying the above condition.

The space of multipliers and convolutors of Orlicz spaces on a locally compact group

Hasan P. Aghababa, Ibrahim Akbarbaglu, Saeid Maghsoudi (2013)

Studia Mathematica

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Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let L φ ( G ) and L ψ ( G ) be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach L φ ( G ) -submodule X of L ψ ( G ) , the multiplier space H o m L φ ( G ) ( L φ ( G ) , X * ) is a dual Banach space with predual L φ ( G ) X : = s p a n ¯ u x : u L φ ( G ) , x X , where the closure is taken in the dual space of H o m L φ ( G ) ( L φ ( G ) , X * ) . We also prove that if φ is a Δ₂-regular N-function, then C v φ ( G ) , the space of convolutors of M φ ( G ) , is identified with the dual of a Banach algebra of functions on G...

Generalized notions of amenability for a class of matrix algebras

Amir Sahami (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the amenability and its related homological notions for a class of I × I -upper triangular matrix algebra, say UP ( I , A ) , where A is a Banach algebra equipped with a nonzero character. We show that UP ( I , A ) is pseudo-contractible (amenable) if and only if I is singleton and A is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of UP ( I , A ) .

Unicellularity of the multiplication operator on Banach spaces of formal power series

B. Yousefi (2001)

Studia Mathematica

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Let β ( n ) n = 0 be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space p ( β ) of all power series f ( z ) = n = 0 f ̂ ( n ) z such that n = 0 | f ̂ ( n ) | p | β ( n ) | p < . We give some sufficient conditions for the multiplication operator, M z , to be unicellular on the Banach space p ( β ) . This generalizes the main results obtained by Lu Fang [1].

On the Aronszajn property for integral equations in Banach space

Stanisław Szufla (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

For the integral equation (1) below we prove the existence on an interval J = [ 0 , a ] of a solution x with values in a Banach space E , belonging to the class L p ( J , E ) , p > 1 . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.

Can ( p ) ever be amenable?

Matthew Daws, Volker Runde (2008)

Studia Mathematica

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It is known that ( p ) is not amenable for p = 1,2,∞, but whether or not ( p ) is amenable for p ∈ (1,∞) ∖ 2 is an open problem. We show that, if ( p ) is amenable for p ∈ (1,∞), then so are ( ( p ) ) and ( ( p ) ) . Moreover, if ( ( p ) ) is amenable so is ( , ( E ) ) for any index set and for any infinite-dimensional p -space E; in particular, if ( ( p ) ) is amenable for p ∈ (1,∞), then so is ( ( p ² ) ) . We show that ( ( p ² ) ) is not amenable for p = 1,∞, but also that our methods fail us if p ∈ (1,∞). Finally, for p ∈ (1,2) and a free ultrafilter over...

L -limited-like properties on Banach spaces

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study weakly precompact sets and operators. We show that an operator is weakly precompact if and only if its adjoint is pseudo weakly compact. We study Banach spaces with the p - L -limited * and the p -(SR * ) properties and characterize these classes of Banach spaces in terms of p - L -limited * and p -Right * subsets. The p - L -limited * property is studied in some spaces of operators.

2-summing multiplication operators

Dumitru Popa (2013)

Studia Mathematica

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Let 1 ≤ p < ∞, = ( X ) n be a sequence of Banach spaces and l p ( ) the coresponding vector valued sequence space. Let = ( X ) n , = ( Y ) n be two sequences of Banach spaces, = ( V ) n , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator M : l p ( ) l q ( ) by M ( ( x ) n ) : = ( V ( x ) ) n . We give necessary and sufficient conditions for M to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞. ...

Renormings of c 0 and the minimal displacement problem

Łukasz Piasecki (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The aim of this paper is to show that for every Banach space ( X , · ) containing asymptotically isometric copy of the space c 0 there is a bounded, closed and convex set C X with the Chebyshev radius r ( C ) = 1 such that for every k 1 there exists a k -contractive mapping T : C C with x - T x > 1 1 / k for any x C .