Nonselfadjoint Operator Algebras, Operator Theory, and Related Topics: The Carl M. Pearcy Anniversary Volume

225 Pages·2012·17.11 MB·English

by  H. Bercovicii

OperatorTheory
Advances and Applications
Vol. 104
Editor:
I. Gohberg
Editorial Office: T. Kailath (Stanford)
School of Mathematical H.G. Kaper (Argonne)
Sciences S.T. Kuroda (Tokyo)
Tel Aviv University P. Lancaster (Calgary)
Ramat Aviv, Israel L.E. Lerer (Haifa)
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Editorial Board: B. Mityagin (Columbus)
J. Arazy (Haifa) V. V. Peller (Manhattan, Kansas)
A. Atzmon (Tel Aviv) J. D. Pincus (Stony Brook)
J. A. Ball (Blacksburg) M. Rosenblum (Charlottesville)
A. Ben-Artzi (Tel Aviv) J. Rovnyak (Charlottesville)
H. Bercovici (Bloomington) D. E. Sarason (Berkeley)
A. Bottcher (Chemnitz) H. Upmeier (Marburg)
L. de Branges (West Lafayette) S. M. Verduyn-Lunel (Amsterdam)
K. Clancey (Athens, USA) D. Voiculescu (Berkeley)
L. A. Coburn (Buffalo) H. Widom (Santa Cruz)
K. R. Davidson (Waterloo, Ontario) D. Xia (Nashville)
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H. Dym (Rehovot)
A. Dynin (Columbus)
P. A. Fillmore (Halifax) Honorary and Advisory
C. Foias (Bloomington) Editorial Board:
P.A.Fuhrmann(BeerShev~ P. R. Halmos (Santa Clara)
S. Goldberg (College Park) T. Kato (Berkeley)
B. Gramsch (Mainz) P. D. Lax (New York)
G. Heinig (Chemnitz) M. S. Livsic (Beer Sheva)
J. A. Helton (La Jolla) R. Phillips (Stanford)
M.A. Kaashoek (Amsterdam) B. Sz.-Nagy (Szeged)
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Editors:
Hari Bercovici and Ciprian L Foias
Department of Mathematics
Indiana University
Bloomington, IN 47405-4301
USA
1991 Mathematics Subject Classification 47-xx, 46L05, 46L30
A CIP catalogue record for this book is available from the
Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Nonselfadjoint operator algebras, operator theory, and related topics : the
Cari M. Pearcy anniversary volume / Hari Bercovici ; Ciprian Foias ed. -
Basel ; Boston; Berlin: Birkhiiuser, 1998
(Operator theory ; VoI. 104)
ISBN 978-3-0348-9771-6 ISBN 978-3-0348-8779-3 (eBook)
DOI 10.1007/978-3-0348-8779-3
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, re-use of ilIustrations, recitation, broadcasting, reproduction on microfilms
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© 1998 Springer Basel AG
Originally published by Birkh!luser Verlag Basel Switzerland in 1998
Softcover reprint ofthe hardcover Ist edition 1998
Printed on acid-free paper produced from chlorine-free pulp. TCF
00
Cover design: Heinz Hiltbrunner, Basel
ISBN 978-3-0348-9771-6
987654321
CONTENTS
EDITORIAL PREFACE VII
PORTRAIT OF CARL PEARCy........................................ viii
CARL M. PEARCY: A BIOGRAPHICAL SKETCH ix
PUBLICATIONS OF CARL M. PEARCY xiii
E. A. AZOFF f3 L. DING,
A good side to non-reflexive transformations 1
H. BERCOVICI, C. FOIAS, f3 A. TANNENBAUM,
On skew Toeplitz operators, 'II ,.......... 23
H. BERCOVICI f3 D. VOICULESCU,
Regularity questions for free convolution 37
S. W. BROWN f3 E. KO,
Operators ofPutinar type 49
R. E. CURTO f3 L. A. FIALKOW, Flat extensions ofpositive
moment matrices: Relations in analytic or conjugate terms 59
R. G. DOUGLAS f3 G. MISRA,
Geometric invariants for resolutions ofHilbert modules 83
G. R. EXNER f3I. B. JUNG,
Some multplicities for contractions with Hilbert-Schmidt defect 113
D W. HADWIN f3 D. R. LARSON, Strong limits ofsimilarities......... 139
A. LAMBERT, LP multipliers and nested Sigma-algebras 147
W. S. LI f3 D. TIMOTIN, On isometric intertwining liftings 155
M. MARSALLI, The predual ofa type I Von Neumann algebra. .......... 169
M. MARTIN f3 N. SALINAS, The canonical complex structure of
flag manifolds in aC*-algebra 173
P. S. MUHLY f3 B. SOLEL,
An algebraic chamcterization ofboundary representations. ........... 189
A. OCTAVIO f3 S. PETROVIC,
Joint spectrum and nonisometric functional calculus 197
EDITORIAL PREFACE
This volume is dedicated to Carl Pearcy on his 60th
birthday. It collects recent contributions to operator
theory, nonselfadjoint operator algebras, measure the
ory, and the theory ofmoments by several ofthe lead
ingspecialists in thoseareas. Manyofthe contributors
are collaborators or former students of Carl Pearcy,
and the variety ofthe topics bears witness to the wide
range of his work and interests.
The editors were helped by many in the compi
lation of this volume. Srdjan Petrovic helped com
pile Carl's list ofpublications, while Arlen Brown and
George Exner helped in writing the biographical and
mathematical sketch. The work ofmany referees, who
must remain anonymous, was very valuable. Israel
Gohberg suggested that we publish this volume in the
distinguished series Operator Theory: Advances and
Applications.
The whole volume was expertly typeset by Elena
Fraboschi. Wewishtoextendto allofthese peopleour
heartfelt thanks.
CARL M. PEARCY

Carl M. Pearcy:
A Biographical Sketch
H. BERCOVICI fj C. FOIAS
Carl Mark Pearcy, Jr. was born on August 23, 1935 in Beaumont, Texas. He was
theeldest oftwosonsofCarl Mark Pearcy, Sr., and CarrieEdith (Tilbury) Pearcy.
His family moved to Galveston in 1940, and that is where Carl resided until he left
home to attend the university. Carl entered Texas A.&M. University in 1951 at
age sixteen. He graduated (B.S.) in 1954 and, again (M.S.) in 1956. Carl entered
Rice Institute (later Rice University) as a candidate for the Ph.D. in Mathematics
in 1956. The degree was conferred in 1960 under the direction of Arlen Brown.
In 1957-58 Carl was a fellow in the mathematics department at the University of
Chicago, and in 1959-60 he held an appointment as Assistant Professor at Texas
A.&M. He was then appointed a post-doctoral fellow at Rice for the year 1960-61.
From1961to 1963CarlwasemployedattheHoustonresearchcenterofHumbleOil
Co. In 1963hewasappointed Assistant ProfessorofMathematicsat the University
ofMichigan, where heremained untilhis "retirement" inthe rank ofFullProfessor
in 1990, at which time he accepted reappointment in the mathematics department
of Texas A.&M. Carl was an A.P. Sloan foundation fellow from 1966 to 1968,
and was the main speaker at two conferences sposored by the Conference Board
of Mathematical Sciences of the National Science Foundation. These conferences
were at Bucknell University in 1975, and Arizona State University in 1984.
While Carl appreciates good mathematics regardless of the field, most of
his mathematical career was closely intertwined with the development of modern
operatortheory. Thereis practicallyno areaofoperatortheory whereCarl did not
contribute. Manyofthese contributionswerefundamental ortrendsetting. We will
highlight just some ofthe most influential ofthese contributions. The numbers in
brackets refer to Carl's publication list.
The characterization ofcommutators, i.e., operators ofthe form T = AB
BA on a Hilbert space was posed as a problem by P. Halmos. It was known that
operators ofthe form zI+C, with z a scalar and C a compact operator, are not
commutators. CarlPearcyand Arlen Brownprovedin [15] that allotheroperators
are in fact commutators. This is one of the earliest deep results pertaining to
arbitraryoperators on a Hilbert space. The methods used in the proofcontain the
germs of the development of the general approximation theory of Hilbert space
operators. In a difft~ent direction, this work led to developments in the theory
of operator algebras. Indeed, it became possible to characterize commutators in
various kinds ofC* andvon Neumannalgebras, andthis also yielded results about
the radical structure ofsuch algebras.
IX