Operator Theory, Analysis and the State Space Approach: In Honor of Rien Kaashoek

499 Pages·2018·6.632 MB·English

by  Harm Bart, Sanne ter Horst, André C.M. Ran, Hugo J. Woerdeman

Operator Theory
Advances and Applications
271
Harm Bart
Sanne ter Horst
André C.M. Ran
Hugo J. Woerdeman
Editors
Operator Theory,
Analysis and
the State Space
Approach
In Honor of Rien Kaashoek

Operator Theory: Advances and Applications
Volume 271
Founded in 1979 by Israel Gohberg

Editors:
Joseph A. Ball (Blacksburg, VA, USA)
Albrecht Böttcher (Chemnitz, Germany)
Harry Dym (Rehovot, Israel)
Heinz Langer (Wien, Austria)
Christiane Tretter (Bern, Switzerland)

Associate Editors: Honorary and Advisory Editorial Board:
Vadim Adamyan (Odessa, Ukraine) Lewis A. Coburn (Buffalo, NY, USA)
Wolfgang Arendt (Ulm, Germany) Ciprian Foias (College Station, TX, USA)
B. Malcolm Brown (Cardiff, UK) J.William Helton (San Diego, CA, USA)
Raul Curto (Iowa, IA, USA) Marinus A. Kaashoek (Amsterdam, NL)
Kenneth R. Davidson (Waterloo, ON, Canada) Thomas Kailath (Stanford, CA, USA)
Fritz Gesztesy (Waco, TX, USA) Peter Lancaster (Calgary, Canada)
Pavel Kurasov (Stockholm, Sweden) Peter D. Lax (New York, NY, USA)
Vern Paulsen (Houston, TX, USA) Bernd Silbermann (Chemnitz, Germany)
Mihai Putinar (Santa Barbara, CA, USA) Harold Widom (Santa Cruz, CA, USA)
Ilya Spitkovsky (Abu Dhabi, UAE)
Subseries
Linear Operators and Linear Systems
Subseries editors:
Daniel Alpay (Orange, CA, USA)
Birgit Jacob (Wuppertal, Germany)
André C.M. Ran (Amsterdam, The Netherlands)

Subseries
Advances in Partial Differential Equations
Subseries editors:
Bert-Wolfgang Schulze (Potsdam, Germany)
Michael Demuth (Clausthal, Germany)
Jerome A. Goldstein (Memphis, TN, USA)
Nobuyuki Tose (Yokohama, Japan)
Ingo Witt (Göttingen, Germany)
More information about this series at http://www.springer.com/series/4850
Harm Bart • Sanne ter Horst • André C.M. Ran
Hugo J. Woerdeman
Editors
Operator Theory, Analysis
and the State Space Approach
In Honor of Rien Kaashoek
Editors
Harm Bart Sanne ter Horst
Econometric Institute Department of Mathematics
Erasmus University Unit for BMI
Rotterdam, The Netherlands North-West University
Potchefstroom, South Africa
André C.M. Ran
Department of Mathematics Hugo J. Woerdeman
Vrije Universiteit Department of Mathematics
Amsterdam, The Netherlands Drexel University
Philadelphia, PA, USA

ISSN 0255-0156 ISSN 2296-4878 (electronic)
Operator Theory: Advances and Applications
ISBN 978-3-030-04268-4 ISBN 978-3-030-04269-1 (eBook)
https://doi.org/10.1007/978-3-030-04269-1

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Preface
On November 10, 2017, M.A. (Rien) Kaashoek turned eighty. Several initia-
tives were taken to celebrate this event. At the Vrije Universiteit in Ams-
terdam a one-afternoon workshop was organized on October 14; at the 2017
IWOTA conference in Chemnitz there was a special session and a plenary
lectureinhonorofRien’supcomingbirthday.ThepresentvolumeintheOp-
erator Theory: Advances and Applications series is also dedicated to Rien’s
eightieth birthday and in celebration of his over fifty years of contributions
to the field of operator theory.
Rien retired from his position as full professor at the Vrije Universiteit
in 2002 at the mandatory retirement age of sixty-five, already having left
a legacy of fifteen Ph.D. students, more than 150 papers, and six research
monographs.Forsomethiswouldhavebeenagoodmomenttostopandfully
enjoy other aspects of life, but not for Rien! On the contrary, even today,
fifteen years after retirement, he is still a very active researcher, as can be
seen from his curriculum vitae, publication list, and list of Ph.D. students,
all of which are included in this volume.
For his many friends and colleagues this is wonderful. With relevant
questions, excellent research problems and discussions, Rien still stimulates
a wide group of researchers. It was therefore no surprise to us when our
invitationstocontributetothisvolumeweremetwithunanimousenthusiasm.
The present volume consists of two parts. The first part contains bio-
graphical information on Rien, his curriculum vitae, publication list, and list
of Ph.D. students referred to above, as well as a few personal reminiscences
fromsomeofhisstudentsandcollaborators.Thesecondpartcompriseseigh-
teenresearchpapersbyRien’scolleagues,collaborators,students,andfriends.
We thank all the authors for the time and efforts they have put into their
contributions,andtheirenthusiasticresponses.Wearealsoveryappreciative
of the dedicated referees, whose input greatly improved the research papers.
This volume is dedicated to Rien, with admiration and gratitude from
his many friends and colleagues around the world.
The editors Harm Bart, Sanne ter Horst,
Andr´e Ran, Hugo Woerdeman
v
Contents
Curriculum Vitae of M.A. Kaashoek ....................................xi
Publication List of M.A. Kaashoek .....................................xv
List of Ph.D. students ...............................................xxxiii
H. Bart, S. ter Horst, D.Pik, A. Ran, F. van Schagen and
H.J. Woerdeman
Personal reminiscenses ...............................................xxxv
J. Agler, Z.A. Lykova and N.J. Young
Carath´eodory extremal functions on the symmetrized bidisc ..............1
J.A. Ball, G.J. Groenewald and S. ter Horst
Standard versus strict Bounded Real Lemma with infinite-dimensional
state space III: The dichotomous and bicausal cases .....................23
H. Bart, T. Ehrhardt and B. Silbermann
L-free directed bipartite graphs and echelon-type canonical forms .......75
J.M. Bogoya, S.M. Grudsky and I.S. Malysheva
Extreme individual eigenvalues for a class of large Hessenberg
Toeplitz matrices ......................................................119
A. B¨ottcher and E. Wegert
How to solve an equation with a Toeplitz operator? ....................145
T. Ehrhardt and Z. Zhou
On the maximal ideal space of even quasicontinuous functions on the
unit circle .............................................................167
Y. Eidelman and I. Haimovici
Bisection eigenvalue method for Hermitian matrices with
quasiseparable representation and a related inverse problem ........... 181
A.E. Frazho and A.C.M. Ran
A note on inner-outer factorization of wide matrix-valued functions ....201
B. Fritzsche, B. Kirstein and C. M¨adler
An application of the Schur complement to truncated matricial
power moment problems ...............................................215
G.J. Groenewald, S. ter Horst, J. Jaftha and A.C.M. Ran
A Toeplitz-like operator with rational symbol having poles on the unit
circle I: Fredholm properties ...........................................239
vii
viii Contents
G.J. Groenewald, D.B. Janse van Rensburg and A.C.M. Ran
Canonical form for H-symplectic matrices .............................269
P. Junghanns and R. Kaiser
A note on the Fredholm theory of singular integral operators with
Cauchy and Mellin kernels .............................................291
J. Nˇemcova´, M. Petreczky and J.H. van Schuppen
Towards a system theory of rational systems ...........................327
L. Plevnik and P. Sˇemrl
Automorphisms of effect algebras ......................................361
A.L. Sakhnovich
GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions
of the corresponding non-stationary problems ..........................389
F.-O. Speck
On the reduction of general Wiener–Hopf operators ....................399
S. Sremac, H.J. Woerdeman and H. Wolkowicz
Maximum determinant positive definite Toeplitz completions ..........421
N. Vasilevski
On commutative C∗-algebras generated by Toeplitz operators with
Tm-invariant symbols ..................................................443
Marinus A. (Rien) Kaashoek in his office at home, 2018
ix
Curriculum Vitae of M.A. Kaashoek
Personal data:
Name: Marinus (Rien) A. Kaashoek
Born: Ridderkerk, The Netherlands; November 10, 1937
Degree: Ph.D., University of Leiden, The Netherlands, 1964;
supervisor: A.C. Zaanen
Married: with Wilhelmina (Wies) E.J. Bakema; three children
Research interests:
Analysisandoperatortheory,andvariousconnectionsbetweenoperatorthe-
ory, matrix theory and mathematical systems theory. In particular, Wiener–
Hopf integral equations and Toeplitz operators and their nonstationary vari-
ants; state space methods for problems in analysis; also metric constrained
interpolation problems, and various extension and completion problems for
partially defined matrices or operators, including relaxed commutant lifting
problems; more recently, inverse problems for orthogonal functions deter-
mined by Toeplitz plus Hankel operators.
Positions:
– Assistant, University of Leiden, 1959–1962.
– Junior staff member, University of Leiden, 1962–1965.
– Postdoc, University of California at Los Angeles, 1965–1966.
– Senior Lecturer, Vrije Universiteit, Amsterdam, 1966–1969.
– Professor, Vrije Universiteit, Amsterdam, 1969–2002.
– Professor Emeritus, Vrije Universiteit, Amsterdam, 2002–present.
Visiting professorships:
– UniversityofMarylandatCollegePark,MD,USA,January–July1975.
– University of Calgary, Calgary, Alberta, Canada, August–September
1981.
– Ben Gurion University of the Negev, Beer Sheva, Israel, April 1987.
– Tel-Aviv University, Tel-Aviv, Israel, various periods.
xi