Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenabilit...Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.展开更多
In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are con...In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.展开更多
In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A =...For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.展开更多
Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely com...Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.展开更多
A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding pr...A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding property belong to just a few special classes (e.g.,amenable algebras and free group factors).In this article,we prove that von Neumann algebras satisfying Popa's co-amenability have Connes's embedding property.展开更多
基金UGC for UGC-SAP-DRS-Ⅱ(Grant No.F.510/3/DRS/2009)provided to the Department of Mathematics,Sardar Patel University,Vallabh Vidyanagar-388120,India
文摘Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.
基金supported by National Natural Science Foundation of China (Grant No. 11226125)
文摘In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
文摘For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.
文摘Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.
文摘A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding property belong to just a few special classes (e.g.,amenable algebras and free group factors).In this article,we prove that von Neumann algebras satisfying Popa's co-amenability have Connes's embedding property.
