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Displaying similar documents to “Unital strongly harmonic commutative Banach algebras”

Isometries between groups of invertible elements in Banach algebras

Osamu Hatori (2009)

Studia Mathematica

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We show that if T is an isometry (as metric spaces) from an open subgroup of the group of invertible elements in a unital semisimple commutative Banach algebra A onto a open subgroup of the group of invertible elements in a unital Banach algebra B, then T ( 1 ) - 1 T is an isometrical group isomorphism. In particular, T ( 1 ) - 1 T extends to an isometrical real algebra isomorphism from A onto B.

Transitivity for linear operators on a Banach space

Bertram Yood (1999)

Studia Mathematica

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Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if x 1 , , x n and y 1 , , y n are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that T ( x k ) = y k , k = 1 , , n . We prove that some proper multiplicative subgroups of G have this property.

Weak amenability of the second dual of a Banach algebra

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

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It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this...

Ideal amenability of module extensions of Banach algebras

Eshaghi M. Gordji, F. Habibian, B. Hayati (2007)

Archivum Mathematicum

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Let 𝒜 be a Banach algebra. 𝒜 is called ideally amenable if for every closed ideal I of 𝒜 , the first cohomology group of 𝒜 with coefficients in I * is zero, i.e. H 1 ( 𝒜 , I * ) = { 0 } . Some examples show that ideal amenability is different from weak amenability and amenability. Also for n N , 𝒜 is called n -ideally amenable if for every closed ideal I of 𝒜 , H 1 ( 𝒜 , I ( n ) ) = { 0 } . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...

Banach spaces which admit a norm with the uniform Kadec-Klee property

S. Dilworth, Maria Girardi, Denka Kutzarova (1995)

Studia Mathematica

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Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space L 2 ( Ӿ ) if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

On certain products of Banach algebras with applications to harmonic analysis

Mehdi Sangani Monfared (2007)

Studia Mathematica

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Given Banach algebras A and B with spectrum σ(B) ≠ ∅, and given θ ∈ σ(B), we define a product A × θ B , which is a strongly splitting Banach algebra extension of B by A. We obtain characterizations of bounded approximate identities, spectrum, topological center, minimal idempotents, and study the ideal structure of these products. By assuming B to be a Banach algebra in ₀(X) whose spectrum can be identified with X, we apply our results to harmonic analysis, and study the question of spectral...

The Kadison problem on a class of commutative Banach algebras with closed cone

M. A. Toumi (2010)

Commentationes Mathematicae Universitatis Carolinae

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The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra A that all of its squares are positive and satisfying the following property: Every continuous bilinear map Φ from A × A into an arbitrary Banach space B such that Φ ( a , b ) = 0 whenever a b = 0 , satisfies the condition Φ ( a b , c ) = Φ ( a , b c ) for all a , b , c A .

An indecomposable Banach space of continuous functions which has small density

Rogério Augusto dos Santos Fajardo (2009)

Fundamenta Mathematicae

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Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight ω < 2 ω such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

The norm spectrum in certain classes of commutative Banach algebras

H. S. Mustafayev (2011)

Colloquium Mathematicae

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Let A be a commutative Banach algebra and let Σ A be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by σ ( f ) = f · a : a A ¯ Σ A , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.

Some remarks on Q -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that p , ( 1 p ) are Q algebras and that A n = L 1 ( Z ; 1 + | n | α ) is a Q -algebra if and only if α &gt; 1 / 2 .

Quasi *-algebras of measurable operators

Fabio Bagarello, Camillo Trapani, Salvatore Triolo (2006)

Studia Mathematica

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Non-commutative L p -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented...