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

M. A. Toumi

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Displaying similar documents to “The Kadison problem on a class of commutative Banach algebras with closed cone”

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 $n \in N$ , $𝒜$ 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.

Derivations with a hereditary domain, II

A. Villena (1998)

Studia Mathematica

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The nilpotency of the separating subspace of an everywhere defined derivation on a Banach algebra is an intriguing question which remains still unsolved, even for commutative Banach algebras. On the other hand, closability of partially defined derivations on Banach algebras is a fundamental problem motivated by the study of time evolution of quantum systems. We show that the separating subspace S(D) of a Jordan derivation defined on a subalgebra B of a complex Banach algebra A satisfies...

An identity with generalized derivations on Lie ideals, right ideals and Banach algebras

Vincenzo de Filippis, Giovanni Scudo, Mohammad S. Tammam El-Sayiad (2012)

Czechoslovak Mathematical Journal

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Let $R$ be a prime ring of characteristic different from $2$ , $U$ the Utumi quotient ring of $R$ , $C = Z (U)$ the extended centroid of $R$ , $L$ a non-central Lie ideal of $R$ , $F$ a non-zero generalized derivation of $R$ . Suppose that $[F (u), u] F (u) = 0$ for all $u \in L$ , then one of the following holds: (1) there exists $α \in C$ such that $F (x) = α x$ for all $x \in R$ ; (2) $R$ satisfies the standard identity $s_{4}$ and there exist $a \in U$ and $α \in C$ such that $F (x) = a x + x a + α x$ for all $x \in R$ . We also extend the result to the one-sided case. Finally, as an application we obtain some range inclusion...

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

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We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where $A = ℓ^{p}$ for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras $ℓ^{p} (ω)$ .

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.

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...

A class of weighted convolution Fréchet algebras

Thomas Vils Pedersen (2010)

Banach Center Publications

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For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that $ω_{m} (t) / ω ₙ (t) \to \infty$ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists...

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 $ℓ^{p}$ , $(1 \leq p \leq \infty)$ are $Q$ algebras and that $A_{n} = ℨ L^{1} (Z; 1 + | n |^{α})$ is a $Q$ -algebra if and only if $α > 1 / 2$ .

A new proof of the noncommutative Banach-Stone theorem

David Sherman (2006)

Banach Center Publications

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Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate...

(Non-)amenability of ℬ(E)

Volker Runde (2010)

Banach Center Publications

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In 1972, the late B. E. Johnson introduced the notion of an amenable Banach algebra and asked whether the Banach algebra ℬ(E) of all bounded linear operators on a Banach space E could ever be amenable if dim E = ∞. Somewhat surprisingly, this question was answered positively only very recently as a by-product of the Argyros-Haydon result that solves the “scalar plus compact problem”: there is an infinite-dimensional Banach space E, the dual of which is ℓ¹, such that $ℬ (E) = (E) + ℂ i d_{E}$ . Still, ℬ(ℓ²) is...