Topological Algebras With Involution

Maria Fragoulopoulou (Eds.)9780444520258, 0444520252

This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.

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Table of contents :
Content:
Introduction
Pages ix-xvi
Maria Fragoulopoulou

Chapter I Background material Original Research Article
Pages 3-98

Chapter II Locally C*—Algebras Original Research Article
Pages 99-141

Chapter III Representation theory Original Research Article
Pages 143-205

Chapter IV Structure space of an m*—Convex algebra Original Research Article
Pages 207-263

Chapter V Hermitian and symmetric topological *—Algebras Original Research Article
Pages 265-315

Chapter VI Integral representations. Uniqueness of topology Original Research Article
Pages 319-361

Chapter VII Tensor products of topological *—Algebras Original Research Article
Pages 363-449

Bibliography Original Research Article
Pages 451-485

Index
Pages 487-495