Displaying similar documents to “On (Co)homology of triangular Banach algebras”

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.

-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 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.

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...

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...

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 < .

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.

Matlis dual of local cohomology modules

Batoul Naal, Kazem Khashyarmanesh (2020)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a commutative Noetherian local ring, 𝔞 be an ideal of R and M a finitely generated R -module such that 𝔞 M M and cd ( 𝔞 , M ) - grade ( 𝔞 , M ) 1 , where cd ( 𝔞 , M ) is the cohomological dimension of M with respect to 𝔞 and grade ( 𝔞 , M ) is the M -grade of 𝔞 . Let D ( - ) : = Hom R ( - , E ) be the Matlis dual functor, where E : = E ( R / 𝔪 ) is the injective hull of the residue field R / 𝔪 . We show that there exists the following long exact sequence 0 H 𝔞 n - 2 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n ( D ( H 𝔞 n ( M ) ) ) D ( M ) H 𝔞 n - 1 ( D ( H 𝔞 n - 1 ( M ) ) ) H 𝔞 n + 1 ( D ( H 𝔞 n ( M ) ) ) H 𝔞 n ( D ( H ( x 1 , ... , x n - 1 ) n - 1 ( M ) ) ) H 𝔞 n ( D ( H ( n - 1 M ) ) ) ... , where n : = cd ( 𝔞 , M ) is a non-negative integer, x 1 , ... , x n - 1 is a regular sequence in 𝔞 on M and, for an R -module L , H 𝔞 i ( L ) is the i th local cohomology module...

( φ , ϕ ) -derivations on semiprime rings and Banach algebras

Bilal Ahmad Wani (2021)

Communications in Mathematics

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Let be a semiprime ring with unity e and φ , ϕ be automorphisms of . In this paper it is shown that if satisfies 2 𝒟 ( x n ) = 𝒟 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒟 ( x ) + 𝒟 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒟 ( x n - 1 ) for all x and some fixed integer n 2 , then 𝒟 is an ( φ , ϕ )-derivation. Moreover, this result makes it possible to prove that if admits an additive mappings 𝒟 , 𝒢 : satisfying the relations 2 𝒟 ( x n ) = 𝒟 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒢 ( x ) + 𝒢 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒢 ( x n - 1 ) , 2 𝒢 ( x n ) = 𝒢 ( x n - 1 ) φ ( x ) + ϕ ( x n - 1 ) 𝒟 ( x ) + 𝒟 ( x ) φ ( x n - 1 ) + ϕ ( x ) 𝒟 ( x n - 1 ) , for all x and some fixed integer n 2 , then 𝒟 and 𝒢 are ( φ , ϕ )derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras. ...

Some homological properties of amalgamated modules along an ideal

Hanieh Shoar, Maryam Salimi, Abolfazl Tehranian, Hamid Rasouli, Elham Tavasoli (2023)

Czechoslovak Mathematical Journal

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Let R and S be commutative rings with identity, J be an ideal of S , f : R S be a ring homomorphism, M be an R -module, N be an S -module, and let ϕ : M N be an R -homomorphism. The amalgamation of R with S along J with respect to f denoted by R f J was introduced by M. D’Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of ( R f J ) -module called the amalgamation of M and N along J with respect to ϕ , and denoted by M ϕ J N . We study some homological properties of the ( R f J ) -module M ϕ J N . Among...

Multiplicative Lie triple derivations on standard operator algebras

Bilal Ahmad Wani (2021)

Communications in Mathematics

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Let 𝒳 be a Banach space of dimension n > 1 and 𝔄 ( 𝒳 ) be a standard operator algebra. In the present paper it is shown that if a mapping d : 𝔄 𝔄 (not necessarily linear) satisfies d ( [ [ U , V ] , W ] ) = [ [ d ( U ) , V ] , W ] + [ [ U , d ( V ) ] , W ] + [ [ U , V ] , d ( W ) ] for all U , V , W 𝔄 , then d = ψ + τ , where ψ is an additive derivation of 𝔄 and τ : 𝔄 𝔽 I vanishes at second commutator [ [ U , V ] , W ] for all U , V , W 𝔄 . Moreover, if d is linear and satisfies the above relation, then there exists an operator S 𝔄 and a linear mapping τ from 𝔄 into 𝔽 I satisfying τ ( [ [ U , V ] , W ] ) = 0 for all U , V , W 𝔄 , such that d ( U ) = S U - U S + τ ( U ) for all U 𝔄 .

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.

Recurrence and mixing recurrence of multiplication operators

Mohamed Amouch, Hamza Lakrimi (2024)

Mathematica Bohemica

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Let X be a Banach space, ( X ) the algebra of bounded linear operators on X and ( J , · J ) an admissible Banach ideal of ( X ) . For T ( X ) , let L J , T and R J , T ( J ) denote the left and right multiplication defined by L J , T ( A ) = T A and R J , T ( A ) = A T , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between T ( X ) , and their elementary operators L J , T and R J , T . In particular, we give necessary and sufficient conditions for L J , T and R J , T to be sequentially recurrent. Furthermore, we prove that L J , T is recurrent...

Annihilators of local homology modules

Shahram Rezaei (2019)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a local ring, 𝔞 an ideal of R and M a nonzero Artinian R -module of Noetherian dimension n with hd ( 𝔞 , M ) = n . We determine the annihilator of the top local homology module H n 𝔞 ( M ) . In fact, we prove that Ann R ( H n 𝔞 ( M ) ) = Ann R ( N ( 𝔞 , M ) ) , where N ( 𝔞 , M ) denotes the smallest submodule of M such that hd ( 𝔞 , M / N ( 𝔞 , M ) ) < n . As a consequence, it follows that for a complete local ring ( R , 𝔪 ) all associated primes of H n 𝔞 ( M ) are minimal.

Some theorems of Korovkin type

Tomoko Hachiro, Takateru Okayasu (2003)

Studia Mathematica

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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, C ( X ) ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., C ( Y ) ), and ϕ a linear isometry from M into C(Y) (resp., C ( Y ) ). We show, under the assumption that Π N Π T , where Π N is...

Strongly ( 𝒯 , n ) -coherent rings, ( 𝒯 , n ) -semihereditary rings and ( 𝒯 , n ) -regular rings

Zhanmin Zhu (2020)

Czechoslovak Mathematical Journal

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Let 𝒯 be a weak torsion class of left R -modules and n a positive integer. A left R -module M is called ( 𝒯 , n ) -injective if Ext R n ( C , M ) = 0 for each ( 𝒯 , n + 1 ) -presented left R -module C ; a right R -module M is called ( 𝒯 , n ) -flat if Tor n R ( M , C ) = 0 for each ( 𝒯 , n + 1 ) -presented left R -module C ; a left R -module M is called ( 𝒯 , n ) -projective if Ext R n ( M , N ) = 0 for each ( 𝒯 , n ) -injective left R -module N ; the ring R is called strongly ( 𝒯 , n ) -coherent if whenever 0 K P C 0 is exact, where C is ( 𝒯 , n + 1 ) -presented and P is finitely generated projective, then K is ( 𝒯 , n ) -projective; the ring R is called...

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.