Semicrossed Products of Operator Algebras by Semigroups ( Memoirs of the American Mathematical Society )

Publication series ：Memoirs of the American Mathematical Society

Author： Kenneth R. Davidson;Adam Fuller;Evgenios T. A. Kakariadis  

Publisher： American Mathematical Society‎

Publication year： 2017

E-ISBN: 9781470423094

P-ISBN(Paperback): 9781470436971

Subject： O177 functional analysis

Keyword： 暂无分类

Language： ENG

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Semicrossed Products of Operator Algebras by Semigroups

Description

The authors examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.

Chapter

Cover

Title page

Chapter 1. Introduction

Chapter 2. Preliminaries

2.1. Operator algebras

2.2. Semigroups

2.3. Completely positive definite functions of groups

2.4. Completely positive definite functions of semigroups

2.5. Lattice-ordered abelian groups

Chapter 3. Semicrossed products by abelian semigroups

3.1. Defining semicrossed products by abelian semigroups

3.2. The unitary semicrossed product

3.3. The isometric semicrossed product

3.4. The contractive semicrossed product by \bZ₊²

3.5. The Fock algebra

Chapter 4. Nica-covariant semicrosssed products

4.1. The regular contractive semicrossed product

4.2. The Nica-covariant semicrossed product

4.3. The Nica-covariant semicrossed product by \bZⁿ₊

4.4. Minimality and ideal structure

4.5. Comparison with C*-correspondences and product systems

Chapter 5. Semicrossed products by non-abelian semigroups

5.1. Possible extensions to non-abelian semigroups

5.2. The semicrossed product by an Ore semigroup

5.3. The semicrossed product by \bF₊ⁿ

Bibliography

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