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Titlebook: Invariant Subspaces; Heydar Radjavi,Peter Rosenthal Book 1973 Springer-Verlag Berlin Heidelberg 1973 Excel.Hilbert space.Invarianter Unter

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发表于 2025-3-21 16:51:54 | 显示全部楼层 |阅读模式
书目名称Invariant Subspaces
编辑Heydar Radjavi,Peter Rosenthal
视频video
丛书名称Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
图书封面Titlebook: Invariant Subspaces;  Heydar Radjavi,Peter Rosenthal Book 1973 Springer-Verlag Berlin Heidelberg 1973 Excel.Hilbert space.Invarianter Unter
描述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 restric
出版日期Book 1973
关键词Excel; Hilbert space; Invarianter Unterraum; addition; analytic function; banach spaces; boundary element
版次1
doihttps://doi.org/10.1007/978-3-642-65574-6
isbn_softcover978-3-642-65576-0
isbn_ebook978-3-642-65574-6
copyrightSpringer-Verlag Berlin Heidelberg 1973
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Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folgehttp://image.papertrans.cn/i/image/474580.jpg
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Shift Operators,are restrictions of bilateral shifts to certain invariant subspaces. The results of this chapter have much wider applicability than this would suggest however, for, as we shall see, every operator is unitarily equivalent to a multiple of a “part” of the adjoint of a unilateral shift.
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Compact Operators, operators have non-trivial invariant subspaces; much more general results are obtained in Chapter 8. We also show that the properties of normality and quasinilpotence for compact operators are determined by their invariant subspaces, and give examples of attainable lattices that are not attainable by compact operators.
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Introduction and Preliminaries,Most of this chapter consists of certain basic definitions and results that will be required later. With the exception of Section 0.4 the results are all very well-known. The reader may wish to use the other sections merely for reference regarding notation.
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Algebras Associated with Invariant Subspaces,In this chapter we consider subalgebras Q of ℬ(ℋ) which are not transitive, and establish certain relations between .Q and various properties of Q. We begin with the following problem.
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