Johnson Pseudo-Contractibility of Certain Banach Algebras and Their Nilpotent Ideals

Askari-Sayah, M.; Pourabbas, A.; Sahami, A.

doi:10.1007/s10476-019-0840-1

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…Note that the notion of Johnson pseudo-contractibility is stronger than pseudo-amenability and it is weaker than pseudo-contractibility. Furthermore the Johnson pseudo-contractibility of various classes of Banach algebras such as, semigroup algebras, Segal algebras and Lipschitz algebras have been studied [15,16] and [2].…”

Section: Introductionmentioning

confidence: 99%

“…A similar result has been given by Grønbaek and Habibian [12], also for a commutative semigroup S; they showed that 1 (S) is biflat if and only if S is a uniformly locally finite semi-lattice of an abelian group. In [2] the authors showed that 1 (S) is not Johnson pseudo-contractible, whenever S is a bicyclic semigroup or S is the semigroup (N, max). Pseudo-contractibility and Johnson pseudo-contractibility of uniformly locally finite inverse semigroups were characterized in [8] and [15], respectively.…”

Section: Introductionmentioning

confidence: 99%

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Johnson pseudo-contractibility of certain semigroup algebras. II

2021

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We investigate Johnson pseudo-contractibility and pseudo-contractibility of Clifford semigroup algebras. We show that, for a Clifford semigroup S, if 1 (S) has a central approximate identity in c 00 (S), then 1 (S) is (Johnson) pseudo-contractible if and only if E(S) is locally finite and each maximal subgroup of S is (amenable) finite, respectively. As an application, we characterize Johnson pseudo-contractibility and pseudo-contractibility of 1 (S), where S is a commutative semigroup, a band semigroup, or an inverse semigroup with totally ordered idempotents set.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Johnson pseudo-contractibility of certain semigroup algebras. II

2021

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On a Notion of Biflatness Related to a Closed Ideal

Sahami,

Ghaderi,

et al. 2024

Journal of Function Spaces

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This study is motivated through the so‐called approximate homology results of Banach algebras arising from their closed ideals. For a Banach algebra , the notion of approximate ‐biflatness is presented, where is a closed ideal of . Moreover, some related results between our concept of homology and the known notions of amenability in the setting of Banach algebras are studied. For a locally compact group G, a necessary and sufficient condition for the measure algebra M(G) to be approximately L1(G)‐biflat is found, where L1(G) is the correspondence group algebra of G. Additionally, some applications of (approximately) ‐biflatness for the Fourier algebras, Lipschitz algebras, and matrix algebras are given. Furthermore, for validation of our concept, some examples for the differences between this new notion and the classical ones are indicated.

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Johnson Pseudo-Contractibility and Pseudo-Amenability of θ-Lau Product

Askari-Sayah

Pourabbas

Sahami

2020

KgJMat

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Given Banach algebras A and B and θ ∈ ∆(B). We shall study the Johnson pseudo-contractibility and pseudo-amenability of the θ-Lau product A×θ B. We show that if A ×θ B is Johnson pseudo-contractible, then both A and B are Johnson pseudo-contractible and A has a bounded approximate identity. In some particular cases, a complete characterization of Johnson pseudo-contractibility of A ×θ B is given. Also, we show that pseudo-amenability of A ×θ B implies the approximate amenability of A and pseudo-amenability of B.

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Johnson Pseudo-Contractibility of Certain Banach Algebras and Their Nilpotent Ideals

Cited by 3 publications

References 17 publications

Johnson pseudo-contractibility of certain semigroup algebras. II

Johnson pseudo-contractibility of certain semigroup algebras. II

On a Notion of Biflatness Related to a Closed Ideal

Johnson Pseudo-Contractibility and Pseudo-Amenability of θ-Lau Product

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