The Gohberg Anniversary Collection: Volume I: The Calgary Conference and Matrix Theory Papers

488 Pages·1989·6.72 MB·English

by  R. S. Phillips (auth.)

OT40
Operator Theory: Advances and Applications
Vol. 40
Editor:
I. Gohberg
Tel Aviv University
Ramat Aviv, Israel
Editorial Office:
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv, Israel
Editorial Board:
A. Atzmon (Tel Aviv) M. A. Kaashoek (Amsterdam)
J. A. Ball (Blacksburg) T. Kailath (Stanford)
L. de Branges (West Lafayette) H. G. Kaper (Argonne)
K. Clancey (Athens, USA) S.T.Kuroda(Tokyo)
L. A. Coburn (Buffalo) P. Lancaster (Calgary)
R. G. Douglas (Stony Brook) L. E. Lerer (Haifa)
H. Dym (Rehovot) E. Meister (Darmstadt)
A. Dynin (Columbus) B. Mityagin (Columbus)
P. A. Fillmore (Halifax) J. D. Pincus (Stony Brook)
C. Foias (Bloomington) M. Rosenblum (Charlottesville)
P. A. Fuhrmann (Beer Sheva) J. Rovnyak (Charlottesville)
S. Goldberg (College Park) D. E. Sarason (Berkeley)
B. Gramsch (Mainz) H. Widom (Santa Cruz)
J.A. Helton (La Jolla) D. Xia (Nashville)
D. Herrero (Tempe)
Honorary and Advisory
Editorial Board:
P. R. Halmos (Santa Clara) S. G. Mikhlin (Leningrad)
T. Kato (Berkeley) R. Phillips (Stanford)
P. D. Lax (New York) B. Sz.-Nagy (Szeged)
M. S. Livsic (Beer Sheva)
Birkhauser Verlag
Basel· Boston· Berlin
The Gohberg Anniversary
Collection
Volume I: The Calgary Conference and
Matrix Theory Papers
Edited by
H.Dym
S. Goldberg
M. A. Kaashoek
P. Lancaster
1989 Birkhauser Verlag
Basel· Boston· Berlin
Volume Editorial Office:
Department of Mathematics
and Computer Science
Vrije Universiteit
Amsterdam, The Netherlands
CIP-TItelaufnahme der Deutschen Bibliothek
The Gohberg anniversary coUection I [vol. ed. office: Dep. of
Mathematics and Computer Science, Vrije Univ., Amsterdam,
The Netherlands]. Ed. by H. Dym ... - Basel; Boston; Berlin
Birkhiiuser
(Operator theory; ... )
ISBN 3-7643-2283-7 (Basel ... )
ISBN 0-8176-2283-7 (Boston)
NE: Dym, Harry [Hrsg.]; Vrije Universiteit <Amsterdam> I Faculteit
derWiskunde en Informatica; Gochberg, Izrail': Festschrift
Vol. 1. The Calgary conference and matrix theory papers. - 1989
The Calgary conference and matrix theory papers I [vol. ed.
office: Dep. of Mathematics and Computer Science, Vrije
Univ., Amsterdam, The Netherlands]. Ed. by H. Dym ... -
Basel ; Boston ; Berlin : Birkhiiuser, 1989
(The Gohberg anniversary collection ; Vol. 1)
(Operator theory ; Vol. 40)
ISBN 3-7643-2307-8 (Basel ... ) Pb.
ISBN 0-8176-2307-8 (Boston)
NE: Dym, Harry [Hrsg.]; 2. GT
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 § 54 of the German Copyright Law where copies are
made for other than private use a fee is payable to NerwertungsgesellschaftWort«, Munich.
© 1989 BirkhiiuserVerlag Basel
Softcover reprint ofthe hardcover 1s t edition 1989
ISBN-13: 978-3-0348-9974-1 e-ISBN-13: 978-3-0348-9276-6
DOl: 10.1007/978-3-0348-9276-6
v
Table of contents of Volume I
Editorial Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
Part A: The Calgary Conference, honoring Israel Gohberg
Portrait I. Gohberg
Acknowledgements 2
The Calgary Conference Program .............................. . 3
Conference picture ................... " ...... . 13
Speech of R.S. Phillips, introducing Israel Gohberg ...... . 15
I. Gohberg
Mathematical tales ......................................... . 17
Four generations .. 57
Gohberg Miscellanea . 5R
The Early Years, hy S. Goldherg 5R
Reminiscences, hy M.G. Krein ................................. . 60
Letter ofA . Markus, N. Krupnik and I. Feldman ..................... . 61
!:Jpeech of R. Duduc/wva, delivered at the hanquet 62
My Years ill Kishinev, hy G. Heinig. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
First Meeting, hy S. Goldherg . . . . . . . . . . . . . . . . . . . . . . . 64
From Two Sides, hy L Lerer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Israel Gohherg at Tel-Aviv University, hy D. Amir . . . . . . . . . . . . . . . . . . . . . . 66
Letter of B. Trachtenhrot ...................................... 6R
The Dutch Connection, hy M.A. KaasllOek .......................... 70
!:Jpeech of L. Frank, delivered dl/ring the conference . . . . . . . . . . . . . . . . . . . . . 71
Gohberg in Canada, hy P Lancaster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Israel at the Weizmann Institute, hy H. Dym . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Letter of B. Khvedelidze, read at the banquet . . . . . . . . . . . . . . . . . . . . . . . . . 77
Speech of M. M. Drzjabashian, delivered at the banquet .................. 77
I. Gohberg with (some of) his co-authors .. 79
I. Gohberg and (former) students 80
Curriculum Vitae ... 81
List of Publications 83
VI
Part B: Papers on Matrix Theory and its Applications
Ando T.. Kubo F.:
Some matrix inequalities in multiport network connections ..... . 111
Bart H.. Thijsse C.Ph.A.:
Complementary triangular forms of upper triangularToeplitz matrices 133
Bhatia R .• Choi M.-D .. Davis Ch.:
Comparing a matrix to its off-diagonal part 151
Cohen N.. iohnson Ch.R .• Rodman L.. Woerdeman H.i.:
Ranks of completions of partial matrices ..... . 165
Davidson K.R.:
Finite dimension problems in operator theory 187
Heinig C .• Rost K.:
Matrices with displacement structure. generalized Bezoutians, and Moebius
transformations ......................................... 203
Kailath T.. Chun 1.:
Generalized Gohberg-Semencul formulas for matrix inversion 231
Lancaster p. Qiang}e.:
Variational properties and Rayleigh quotient algorithms for symmetric matrix
pencils ............................................... 247
Lerer L.:
The matrix quadratic equation and factorization of matrix polynomials 279
Nelis H.. Dewilde p. Deprettere E.:
Inversion of partially specified positive definite matrices by inverse scattering 325
v.:
Pan
Fast and efficient parallel inversion ofT oe piitz and blockToeplitz matrices 359
RanA.CM. • Rodman L.:
Stability of invariant lagrangian subspaces II 391
RanA.CM. • Roozemond L.:
On strong a-stability of invariant subspaces of matrices 427
Reichstein B.:
On classification of invariant subspaces of a linear operator 437
Rozsa p. Bevilacqua. R .• Favati p. Romani F.:
On the inverse of block tridiagonal matrices with applications to the inverses
of band matrices and block band matrices . . . . . . . . . . . . . . . . . . . . . . . . . 447
Thompson R. C :
Divisibility relations satisfied by the invariant factors of a matrix product 471
Table of contents of Volume II ................................. 493
VII
Editorial Preface
The Gohberg Anniversary Collection is dedicated to Israel Gohberg. It contains the
proceedings of the international conference on "Operator Theory: Advances and Applications",
which was held in Calgary, August 22 -26, 1988, on the occasion of his 60th birthday. The two
volwnes present an up to date and attractive account of recent advances in operator theory, matrix
theory and their applications. They include contributions by a number of the world's leading
specialists in these areas and cover a broad spectrwn of topics, many of which are on thefrontiers
of reseach. The two volwnes are a tribute to Israel Gohberg; they reflect the wide range of his
mathematical initiatives and personal interests.
This first volwne is split into two parts. The first part consists of "Mathematical Tales"
by I. Gohberg and a biographical text composed by the Editors from letters written by Gohberg's
former colleagues and co-workers in Kishinev, from speeches delivered at the conference andfrom
various personal notes, including "Reminiscences" by M.G. Krein. This part also contains
Gohberg's curriculwn vitae, his list ofp ublications and the Calgary Conference program.
The second part of this volwne consists of papers on matrix theory and its applications.
It includes original research papers on Toeplitz matrices and other specific classes of structured
matrices, on efficient inversion of matrices and problems in numerical linear algebra, on completion
problems for partially defined matrices, on stability and classification of invariant subspaces, and
the study of invariant factors.
The Editors are grateful to the Department of Mathematics and Computer Science of the
Vrije U nversiteit for providing secretarial assistance. In particular, they thank Marijke Titawano for
her work.
The Editors
Part A
The Calgary Conference, honoring Israel Gohberg
on the occasion of his 60th birthday
Israel Gohberg
2
Acknowledgements
These anniversary volumes owe their existence to the conference on "Operator Theory:
Advances and Applications", held in honour of Israel Gohberg's 60th birthday at the University of
Calgary, Canada, from August 22nd to 26th, 1988. This conference was made possible by the
financial support of:
The National Sciences and Engineering Research Council, Canada,
The National Science Foundation, U.S.A.,
The Office of Naval Research, U.S.A.,
The United States Army,
The University of Calgary,
Control Data, Canada,
Nathan and Lily Silver, Israel,
as well as by the willingness of many invited participants to seek other sources of funding. The
help of all these agencies and individuals is gratefully acknowledged by the organizers.
The organizers would also like to record their thanks to several individuals at the
University of Calgary for their support of the conference in various forms. To PJ. Krueger, Vice
President Academic for his opening address. To Dean D.A. Armstrong of the Faculty of Science
for financial support of the social program. To P.I. Browne, Head of the Department of
Mathematics and Statistics for support and assistance in meeting substantial over-head costs. To
lim Peacock of the Department of Communications Media for excellent group phothographs, some
of which appear in this volume. To Madeleine Aldridge of the Conference Office and her staff for
their cheerful assistance through many months of preparations, and to Lome Williams of "Summer
Conference Housing" for his friendly and accomodating approach to a difficult task.
International Orf:anizinf: Commjttee:
P. Lancaster, Chairman, The University of Calgary,
H. Dym, Weizmann Institute,
S. Goldberg, University of Maryland,
M.A. Kaashoek, Vrije Universiteit, Amsterdam.
With the assitstance of:
H. Bart (Rotterdam), I.A.Ball (Blacksburg), C. Foias (Bloomington),
I.W. Helton (San Diego), L. Lerer (Haifa), L. Rodman (Williamsburg).
Local Orf:anizinf: Committee:
P. Lancaster (Chairman), PJ. Browne, P.A. Binding,
Madeleine Aldridge (for the Conference Office).