Invariant Subspaces

✍ Scribed by Heydar Radjavi, Peter Rosenthal (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1973
• Tongue: English
• Leaves: 230
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 77
• Edition: 1
• Category: Library

✦ Synopsis

In recent years there has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self-adjoint of the results have been obtained in operators on Hilbert space. Some the context of certain general studies: the theory of the characteristic operator function, initiated by Livsic; the study of triangular models by Brodskii and co-workers; and the unitary dilation theory of Sz.­ Nagy and Foia!? Other theorems have proofs and interest independent of any particular structure theory. Since the leading workers in each of the structure theories have written excellent expositions of their work, (cf. Sz.-Nagy-Foia!? [1], Brodskii [1], and Gohberg-Krein [1], [2]), in this book we have concentrated on results independent of these theories. We hope that we have given a reasonably complete survey of such results and suggest that readers consult the above references for additional information. The table of contents indicates the material covered. We have restricted ourselves to operators on separable Hilbert space, in spite of the fact that most of the theorems are valid in all Hilbert spaces and many hold in Banach spaces as well. We felt that this restriction was sensible since it eases the exposition and since the separable-Hilbert­ space case of each of the theorems is generally the most interesting and potentially the most useful case.

✦ Table of Contents

Front Matter....Pages I-XI
Introduction and Preliminaries....Pages 1-10
Normal Operators....Pages 11-25
Analytic Functions of Operators....Pages 26-35
Shift Operators....Pages 36-59
Examples of Invariant Subspace Lattices....Pages 60-83
Compact Operators....Pages 84-94
Existence of Invariant and Hyperinvariant Subspaces....Pages 95-116
Certain Results on von Neumann Algebras....Pages 117-137
Transitive Operator Algebras....Pages 138-166
Algebras Associated with Invariant Subspaces....Pages 167-191
Some Unsolved Problems....Pages 192-198
Back Matter....Pages 199-222

✦ Subjects

Mathematics, general