Customer Reviews

An Introduction to Models and Decompositions in Operator Theory

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The book is a very nice introduction to the subject of Models and Decompositions of operators. In reality, it is a post-introductory book. Anyone that has already studied operator Theory in Hilbert spaces and wants a deeper understanding of this subject, should have a look here, mainly because the book coherently organizes this subject that would otherwise require a large bibliographical research. Models and Decompositons are looked as a sub-product of the search for the "Holy Graal" of operator theory: The Invariant Subspace Problem. Although it is not a book about that subject, it is certainly a relevant book to anyone entering that field, because it mentions relatively recent results that were previously conjectures in that area. Particularly interesting, in my opinion, are chapters 7 and 8. Chapter 7, called "Applications", in which the theory developed in the previous chapters is applied and many interesting related problems, some of them still open, relative to strong and weak stability of operators are mentioned. Chapter 8 discusses the problem of similarity to contractions, and leaves the reader with two related open questions.