rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems,...

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall...

The present book is an expanded and enriched version ofthe textBasicOperator Theory, written by the first two authors more than twenty years ago. Since then the three ofus have used the basic operator theory text in various courses. This experience motivated us to update and improve the old text by including a wider variety ofbasic classes ofoperators and their applications. The present book has also been written in such a way that it can serve as an introduction to our previous booksClassesofLinearOperators, Volumes I and II. We view the three books as a unit. We gratefully acknowledge the...

R. S. PHILLIPS I am very gratified to have been asked to give this introductory talk for our honoured guest, Israel Gohberg. I should like to begin by spending a few minutes talking shop. One of the great tragedies of being a mathematician is that your papers are read so seldom. On the average ten people will read the introduction to a paper and perhaps two of these will actually study the paper. It's difficult to know how to deal with this problem. One strategy which will at least get you one more reader, is to collaborate with someone. I think Israel early on caught on to this, and I...

This - book offers a panoptic view of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive...

This book is dedicated to a theory of traces and determinants on embedded algebras of linear operators, where the trace and determinant are extended from finite rank operators by a limit process. The self-contained material should appeal to a wide group of mathematicians and engineers, and is suitable for teaching.

These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and...

R. S. PHILLIPS I am very gratified to have been asked to give this introductory talk for our honoured guest, Israel Gohberg. I should like to begin by spending a few minutes talking shop. One of the great tragedies of being a mathematician is that your papers are read so seldom. On the average ten people will read the introduction to a paper and perhaps two of these will actually study the paper. It's difficult to know how to deal with this problem. One strategy which will at least get you one more reader, is to collaborate with someone. I think Israel early on caught on to this, and I...

In this article we shall use two special classes of reproducing kernel Hilbert spaces (which originate in the work of de Branges [dB) and de Branges-Rovnyak [dBRl), respectively) to solve matrix versions of a number of classical interpolation problems. Enroute we shall reinterpret de Branges' characterization of the first of these spaces, when it is finite dimensional, in terms of matrix equations of the Liapunov and Stein type and shall subsequently draw some general conclusions on rational m x m matrix valued functions which are "J unitary" a.e. on either the circle or the line. We shall...