Fréchet algebras of global dimension zero

Selivanov, Yu. V.

doi:10.1515/9783110813418-025

Cited by 9 publications

(12 citation statements)

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“…In this paper, we study basic properties of amenability modulo an ideal such as virtual diagonal modulo an ideal, approximate diagonal modulo an ideal, and contractible modulo an ideal. Among other results, we show that the semigroup algebra 1 ( ) is contractible modulo an ideal if and only if / is finite, restoring Selivanov's theorem for a large class of semigroups [7].…”

Section: Introductionsupporting

confidence: 65%

Amenability and Contractibility Modulo an Ideal of Banach Algebras

Rahimi

Tahmasebi

2014

Abstract and Applied Analysis

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We investigate the concept of amenability modulo an ideal of Banach algebra, showing that amenability modulo an ideal can be characterized by the existence of virtual and approximate diagonal modulo an ideal. We also study the concept of contractible modulo an ideal of Banach algebra. As a consequence, we prove a version of Selivanov's theorem for a large class of semigroups, includingE-inversiveE-semigroup and eventually inverse semigroups.

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Section: Introductionsupporting

confidence: 65%

Amenability and Contractibility Modulo an Ideal of Banach Algebras

Rahimi

Tahmasebi

2014

Abstract and Applied Analysis

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“…The simplest example of a contractible topological algebra is the C * -algebra M n (C) of all complex n × n-matrices (the full matrix algebra). J. L. Taylor noticed in 1972 (see [93, p. 181]; for a proof see [84,Lemma 11]) that a topological Cartesian product of full matrix algebras is a contractible algebra.…”

Section: Some Definitions and Results Concerning Topological Algebrasmentioning

confidence: 99%

Structure theory of homologically trivial and annihilator locally C^*-algebras

Pirkovskii

Selivanov

2010

Banach Center Publ.

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We study the structure of certain classes of homologically trivial locally C * -algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a locally C * -algebra, then all irreducible Hermitian A-modules are projective if and only if A is a direct topological sum of elementary C * -algebras. This is also equivalent to A being an annihilator (dual, complemented, left quasi-complemented, or topologically modular annihilator) topological algebra. We characterize all annihilator σ-C * -algebras and describe the structure of biprojective locally C * -algebras. Also, we present an example of a biprojective locally C * -algebra that is not topologically isomorphic to a Cartesian product of biprojective C * -algebras. Finally, we show that every superbiprojective locally C * -algebra is topologically * -isomorphic to a Cartesian product of full matrix algebras.

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“…Основным направлением ис-следования бипроективных алгебр было и остается исследование оказавшегося непростым вопроса об их внутреннем строении (см. [3]- [6]). …”

Section: Introductionunclassified