On $\phi$-biflat and $\phi$-biprojective Banach algebras

Sahami, A.; Pourabbas, A.

doi:10.36045/bbms/1385390764

Cited by 21 publications

(13 citation statements)

References 7 publications

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“…In [17], the authors studied φ-biflatness of group algebras. In this section we continue the study of φ-biflatness of Segal algebras and the second duals of group algebras.…”

Section: φ-Biflatnessmentioning

confidence: 99%

“…The concepts of φ-biflatness, φ-biprojectivity, φ-Johnson amenability and other related concepts were introduced and studied in [17]. The studies include determining when the various classes of Banach algebras are, or are not φ-biflat or φ-biprojective.…”

Section: Introductionmentioning

confidence: 99%

“…The studies include determining when the various classes of Banach algebras are, or are not φ-biflat or φ-biprojective. It was shown in [17] that L 1 (G) is φ-biflat if and only if G is an amenable group and the Fourier algebra A(G) is φ-biprojective if and only if G is a discrete group.…”

Section: Introductionmentioning

confidence: 99%

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Approximate biprojectivity and $\phi $-biflatness of certain Banach algebras

Sahami

Pourabbas

2016

Colloq. Math.

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In this paper, we study left φ-biflatness and left φ-biprojectivity of some Banach algebras, where φ is a non-zero multiplicative linear function. We show that if the Banach algebra A * * is left φ-biprojective, then A is left φ-biflat. Using this tool we study left φbiflatness of some matrix algebras. We also study left φ-biflatness and left φ-biprojectivity of the projective tensor product of some Banach algebras. We prove that for a locally compact2010 Mathematics Subject Classification. Primary 46M10, 46H05 Secondary 43A07, 43A20.

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“…In [17], the authors studied φ-biflatness of group algebras. In this section we continue the study of φ-biflatness of Segal algebras and the second duals of group algebras.…”

Section: φ-Biflatnessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate biprojectivity and $\phi $-biflatness of certain Banach algebras

Sahami

Pourabbas

2016

Colloq. Math.

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“…Right cases define similarly. For more information about these new concepts of amenability and its related homological notions see [1], [17], [14] and [22].…”

Section: Converse Is Clearmentioning

confidence: 99%

Generalized notion of amenability for a class of matrix algebras

Sahami

2016

Preprint

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We investigate the notions of amenability and its related homological notions for a class of I × I-upper triangular matrix algebra, say U P (I, A), where A is a Banach algebra equipped with a nonzero character. We show that U P (I, A) is pseudo-contractible (amenable) if and only if I is singleton and A is pseudo-contractible (amenable), respectively. We also study the notions of pseudo-amenability and approximate biprojectivity of U P (I, A).Recently approximate versions of amenability and homological properties of Banach algebras have been under more observations. In [24] Zhang introduced the notion of approximately biprojective Banach algebras, that is, A is approximately biprojective if there exists a net of A-bimodule morphism ρAuthor with A. Pourabbas investigated approximate biprojectivity of 2 × 2 upper triangular Banach algebra which is a matrix algebra, also we characterized approximate biprojectivity of Segal algebras and weighted group algebras. We show that a Segal algebra S(G) is approximately biprojective if and only if

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“…For a locally compact group G, we showed that Segal algebra S(G) is φ−biflat(biprojective) if and only if G is amenable(compact). Also A(G) is φ-biprojective if and only if G is discrete, see [19] and [21].…”

Section: Introductionmentioning

confidence: 99%

On approximate left φ-biprojective Banach algebras

Sahami

Pourabbas

2018

Glas. Mat. Ser. III

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Abstract. Let A be a Banach algebra. We introduce the notions of approximate left φ-biprojective and approximate left character biprojective Banach algebras, where φ is a non-zero multiplicative linear functional on A. We show that for a SIN group G, the Segal algebra S(G) is approximate left φ 1 -biprojective if and only if G is amenable, where φ 1 is the augmentation character on S(G). Also we show that the measure algebra M (G) is approximate left character biprojective if and only if G is discrete and amenable. For a Clifford semigroup S, we show that ℓ 1 (S) is approximate left character biprojective if and only if ℓ 1 (S) is pseudo-amenable. We study the hereditary property of these notions. Finally we give some examples to show the differences of these notions and the classical ones.

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On $\phi$-biflat and $\phi$-biprojective Banach algebras

Cited by 21 publications

References 7 publications

Approximate biprojectivity and $\phi $-biflatness of certain Banach algebras

Approximate biprojectivity and $\phi $-biflatness of certain Banach algebras

Generalized notion of amenability for a class of matrix algebras

On approximate left φ-biprojective Banach algebras

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