TO THE SECOND EDITION Since publication of the First Edition
several excellent treatments of advanced topics in analysis have
appeared. However, the concentration and penetration of these
treatises naturally require much in the way of technical
preliminaries and new terminology and notation. There consequently
remains a need for an introduction to some of these topics which
would mesh with the material of the First Edition. Such an
introduction could serve to exemplify the material further, while
using it to shorten and simplify its presentation. It seemed
particularly important as well as practical to treat briefly but
cogently some of the central parts of operator algebra and higher
operator theory, as these are presently represented in book form
only with a degree of specialization rather beyond the immediate
needs or interests of many readers. Semigroup and perturbation
theory provide connections with the theory of partial differential
equations. C*-algebras are important in har monic analysis and the
mathematical foundations of quantum mechanics. W*-algebras (or von
Neumann rings) provide an approach to the theory of multiplicity of
the spectrum and some simple but key elements of the gram mar of
analysis, of use in group representation theory and elsewhere. The
v vi Preface to the Second Edition theory of the trace for
operators on Hilbert space is both important in itself and a
natural extension of earlier integration-theoretic ideas."
General
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