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

M. A. Toumi

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 $ℓ^{p} (ω)$ .

Character Connes amenability of dual Banach algebras

Mohammad Ramezanpour (2018)

Czechoslovak Mathematical Journal

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We study the notion of character Connes amenability of dual Banach algebras and show that if $A$ is an Arens regular Banach algebra, then $A^{* *}$ is character Connes amenable if and only if $A$ is character amenable, which will resolve positively Runde’s problem for this concept of amenability. We then characterize character Connes amenability of various dual Banach algebras related to locally compact groups. We also investigate character Connes amenability of Lau product and module extension...

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...