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Amenability and weak amenability of ...

Zhang, Yong.

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Amenability and weak amenability of Banach algebras.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Amenability and weak amenability of Banach algebras./
Author:	Zhang, Yong.
Description:	111 p.
Notes:	Source: Dissertation Abstracts International, Volume: 60-09, Section: B, page: 4652.
Contained By:	Dissertation Abstracts International60-09B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ41635
ISBN:	0612416356

Amenability and weak amenability of Banach algebras.
Zhang, Yong.

Amenability and weak amenability of Banach algebras. - 111 p.

Source: Dissertation Abstracts International, Volume: 60-09, Section: B, page: 4652.

Thesis (Ph.D.)--University of Manitoba (Canada), 1999.

We start with the investigation of (2m)-th conjugate algebras of Banach algebras (equipped with Arens products) and related higher order dual Banach modules. In the process we explore important properties of the higher order dual operators of modulemorphisms and of derivations. After this basic investigation we consider various problems in or related to the theory of amenability and weak amenability of Banach algebras. The work is described by the following three themes:

ISBN: 0612416356Subjects--Topical Terms:

515831
Mathematics.

Amenability and weak amenability of Banach algebras.
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020 $a 0612416356
035 $a (UnM)AAINQ41635
035 $a AAINQ41635
040 $a UnM $c UnM
100 1 $a Zhang, Yong. $3 718280
245 1 0 $a Amenability and weak amenability of Banach algebras.
300 $a 111 p.
500 $a Source: Dissertation Abstracts International, Volume: 60-09, Section: B, page: 4652.
500 $a Adviser: F. Ghahramani.
502 $a Thesis (Ph.D.)--University of Manitoba (Canada), 1999.
520 $a We start with the investigation of (2m)-th conjugate algebras of Banach algebras (equipped with Arens products) and related higher order dual Banach modules. In the process we explore important properties of the higher order dual operators of modulemorphisms and of derivations. After this basic investigation we consider various problems in or related to the theory of amenability and weak amenability of Banach algebras. The work is described by the following three themes:
520 $a Theme 1. Weak amenability of Banach algebras. We first discuss the conditions under which n-weak amenability implies (n + 2)-weak amenability for n > 0, and the conditions for the unitization of a Banach algebra to be n-weakly amenable. After an extensive study of module extensions of Banach algebras, we give a necessary and sufficient condition for a Banach algebra of this kind to be n-weakly amenable, separately for odd numbers n and even numbers n. Then we discuss several concrete cases, especially those related to operator algebras. These finally offer us a way to construct a counter-example to the open question of whether weak amenability implies 3-weak amenability.
520 $a Theme 2.{09}Structure of contractible Banach algebras and amenable Banach algebras with the underlying spaces reflexive. By exploiting properties of minimal idempotents we show that a Banach algebra of this kind is finite dimensional if every maximal ideal of it is contained in a maximal left ideal which is complemented as a subspace. This result improves several known results concerning the subject.
520 $a Theme 3. Nilpotent ideals in a class of Banach algebras. We introduce the concept of approximately complemented subspaces in a Banach space. Then we discuss the relation between this notion and some well-known ones like approximation property and weak complementability. The category of this notion includes many interesting cases. Tensor products of subspaces of this kind have some natural properties. We prove that in a class of Banach algebras called approximately biprojective Banach algebras, nilpotent ideals, if any, lack certain geometric properties such as being approximately complemented.
590 $a School code: 0303.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a University of Manitoba (Canada). $3 1018707
773 0 $t Dissertation Abstracts International $g 60-09B.
790 1 0 $a Ghahramani, F., $e advisor
790 $a 0303
791 $a Ph.D.
792 $a 1999
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NQ41635