Preface

Abstract

This chapter presents preface to the book that intended to give access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The questions of what one mean by ‘continuous linear representations' and by the emphasis on general Lie groups are clarified by the Introduction by the book. The focus is placed on continuous representations over Banach spaces (the duals of such also encompass the important special case of separately weak continuous representations over von Neumann algebras). The Chapter discusses the basic theory of unitary representations: the induced representations of Mackey, representations of commutative, and of compact groups; the theory of one-parameter semigroups over Banach spaces; and the integrability theorems of infinitesimal representations.