Biflatness and Biprojectivity of Banach Algebras Graded Over a Semilattice

Grønbæk, Niels; Habibian, F.

doi:10.1017/s0017089510000364

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…In [4] Choi showed that for a Clifford semigroup S, 1 (S) is biflat if and only if E(S) is uniformly locally finite and each maximal subgroup of S is amenable. 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).…”

Section: Introductionsupporting

confidence: 76%

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: Introductionsupporting

confidence: 76%

Johnson pseudo-contractibility of certain semigroup algebras. II

2021

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“…we deduce that X A X A is biflat [10,Proposition 3.3]. (ii) By assumption X is an essential two-sided ideal of X A and by [11,Proposition 8], it follows that X is biflat.…”

Section: Pseudo-contractibility Of θ-Lau Product Of Banach Algebrasmentioning

confidence: 99%

Characterization of homological properties of θ-Lau product of Banach algebras

Essmaili

Rejali

Salehi

2021

Filomat

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Let A and B be two Banach algebras and ?? ?(B): In this paper, we investigate biprojectivity and biflatness of ?-Lau product of Banach algebras A x? B. Indeed, we show that A x? B is biprojective if and only if A is contractible and B is biprojective. This generalizes some known results. Moreover, we characterize biflatness of ?-Lau product of Banach algebras under some conditions. As an application, we give an example of biflat Banach algebras A and X such that the generalized module extension Banach algebra X o A is not biflat. Finally, we characterize pseudo-contractibility of ?-Lau product of Banach algebras and give an affirmative answer to an open question.

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Biprojectivity of generalized module extension and second dual of Banach algebras

2021

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In this paper, we study biprojectivity of generalized module extension Banach algebras and second dual of Banach algebras. As a main result, we prove that if [Formula: see text] is a contractible closed ideal of [Formula: see text] such that [Formula: see text] is biprojective, then [Formula: see text] is biprojective. As a consequence, we give some results on biprojectivity of generalized module extension Banach algebras. Indeed, this is a generalization of results in [A. Ebaddian and A. Jabbari, Biprojectivity and biflatness of amalgamated duplication of Banach algebras, J. Algebra Its Appl. 19(7) (2020) 2050132 (15 pp.)]. Moreover, we show that if [Formula: see text] is biprojective and [Formula: see text] is a two-sided ideal of [Formula: see text] then [Formula: see text] is biprojective. This fact generalizes some known results in [M. S. Moslehian and A. Niknam, Biflatness and biprojectivity of second dual of Banach algebras, Southeast Asian Bull. Math 27(1) (2003) 129–133].

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Biflatness and Biprojectivity of Banach Algebras Graded Over a Semilattice

Abstract: Abstract. We give sufficient conditions and necessary conditions for a Banach algebra, which is 1 −graded over a semi-lattice, to be biflat or biprojective. As an application we characterise biflat and biprojective discrete convolution algebras for commutative semi-groups.

Cited by 3 publications

References 11 publications

Johnson pseudo-contractibility of certain semigroup algebras. II

Johnson pseudo-contractibility of certain semigroup algebras. II

Characterization of homological properties of θ-Lau product of Banach algebras

Biprojectivity of generalized module extension and second dual of Banach algebras

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