Seminormal Operators
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742
Kevin Clancey
Seminormal Operators
Springer-Verlag Berlin Heidelberg New York 1979
Author Kevin Clancey Department of Mathematics University of Georgia Athens, G A 3 0 6 0 2 USA
A M S Subject Classifications (1970): 47 B20, 4 7 A 6 5 ISBN 3 - 5 4 0 - 0 9 5 4 7 - 0 Springer-Verlag Berlin Heidelberg NewYork ISBN 0 - 3 8 ? - 0 9 5 4 7 - 0 Springer-Verlag NewYork Heidelberg Berlin Library of Congress Cataloging in Publication Data Clancey, Kevin, 1944Seminormal operators. (Lecture notes in mathematics; 742) Bibliography: p. Includes index. 1. Subnormal operators. I. Title. II. Series: Lecture notes in mathematics (Berlin); 742. QA3.L28 no. 742 [QA329.2] 510'.8s [515'.72] 79-20324 ISBN 0-387-09547-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under £354 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
Preface
These space.
notes
In the
operators created
have
stirs
(at least)
of
decade
been
obtained,
five
interest
with
several
the
is h a p p e n i n g .
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major
area.
sources
self-contained
seminormal
and
this
The
aim
of
which
have
on
appear
These
picture
operators
operators
results
some of w h i c h
in
different
what
a reasonably
concerned
past
of
to a p p r e c i a t e
area
are
of
some
this
it
these of
the
occurred
a Hilbert
class
mystifying
results
makes
on
have
and come
somewhat notes
of
from
difficult
is to p a i n t
developments
during
have
the
in t h e
last
ten
years. The in
1970
fact when
measure
A.
C.
of the
positive. C.
that
and
with
operators
PUTNAM
established
spectrum
Perhaps
BERGER
operator
R.
seminormal
a cyclic
two
PINCUS
studying
function)
for
invariant
arose
the
theory
HELTON and
of
as
began
in an o p e r a t o r introduced
a tracial
sented
via
integration
Pincus
immediately
principal
function.
a trace
form
up a g a i n s t
verified
this
on
CAREY
the
of
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phase
the
work
generated
by
D.
a signed
measure
on t h e
have
shift
of
from
Carey
These
which
derivative
This
polynomials
algebra
authors
J.
operators.
this
these
and
principal
self-adjoint
has
by
hyponormal
self-commutator.
measure
Independently,
R. W.
to u n d e r s t a n d
class
1973
self-commutator.
analogue of
in
is
self-cor~mutator.
to as
star-algebra
a trace
bilinear
place
class
perturbations
the
class
any
obvious
Lebesgue
operator
obtained
that
(referred
in an a t t e m p t
has
shows
taking
dimensional
studying
that
result
bec
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