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Book review

Author(s) Branges, L. de (ed.)
Gohberg, I. (ed.)
Rovnyak, J. (ed.)
Title Topics in Operator Theory, Ernst D. Hellinger Memorial Volume
Publisher Birkhäuser
Year of publication 1990
Reviewed by Michal Zajac

This is a volume honoring Ernst Hellinger (1883-1950). In a very interesting introductory paper James Rovnyak describes the life and work of Ernst Hellinger. Hellinger's sister Hanna Meissner contributed a nice article entitled "How I, at age 92, remember my brother, 38 years after his death."

The volume contains 19 papers on various topics in Operator theory:

J. Agler: On the representation of certain holomorphic functions defined on a polydisc.

J. Arazy, D. Fisher: Invariant Hilbert spaces of analytic functions on bounded symmetric domains.

J.A. Ball, T.R. Fanney: Closability of differential operators and real subjordan operators.

A. Ben-Artzi, I. Gohberg, M.A. Kaashoek: Invertibility and dichotomy of singular difference equations.

H. Bercovici: On the iterates of a completely nonunitary contraction.

A. Bötcher, S. Roch, B. Silbermann, I.M. Spitkovskii: A Gohberg-Krupnik-Sarason symbol calculus for algebras of Toeplitz, Hankel, Cauchy and Carleman operators.

D.N. Clark: Perturbation and similarity of Toeplitz operators.

T. Constantinescu: Factorization of positive-definite kernels.

A. Dijksma, H. Langer, H. De Snoo: Generalized coresolvents of standard isometric operators and generalized resolvents of standard symmetric relations in Krein spaces.

A. Ghondea: On the structure of linear contractions with respect to fundamental decompositions.

T. Jech: Local topology and spectral theorem.

T.L. Kriete III: Isometries from the Laguerre shift.

H. Langer, R. Mennicken, M. Möller: A second order differential operator depending nonlinearly on the eigenvalue parameter.

D. Sarason: Exposed points in H1, II.

Yu.L. Shmul'yan: Functional completeness of definite subspaces in Krein space.

G. Stolz: Expansion in generalized eigenfunctions of Schrödinger operators with singular potentials.

S. Sun: Duality and Hankel operators.

H. Widom: Eigenvalue distribution of non-selfadjoint Toeplitz matrices and the asymptotics of Toeplitz determinants in the case of nonvanishing index.

D. Xia: On some classes of hyponormal tuples of commuting operators.

Most of these articles presents deep new results. Probably only a few specialists will buy this book for their personal library, but every mathematical library should have this volume.