The Resource An Introduction to Models and Decompositions in Operator Theory, by Carlos S. Kubrusly, (electronic resource)

An Introduction to Models and Decompositions in Operator Theory, by Carlos S. Kubrusly, (electronic resource)

Label
An Introduction to Models and Decompositions in Operator Theory
Title
An Introduction to Models and Decompositions in Operator Theory
Statement of responsibility
by Carlos S. Kubrusly
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
By a Hilbert-space operator we mean a bounded linear transformation be­ tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in­ variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op­ erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite­ dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters
http://library.link/vocab/creatorName
Kubrusly, Carlos S
Dewey number
515.724
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
Fi_x2wvVepM
Image bit depth
0
Language note
English
LC call number
QA329-329.9
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Operator theory
  • Mathematics
  • Operator Theory
  • Mathematical Modeling and Industrial Mathematics
  • Applications of Mathematics
Label
An Introduction to Models and Decompositions in Operator Theory, by Carlos S. Kubrusly, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
0. Preliminaries -- 0.1. Hilbert-Space Operators -- 0.2. Spectrum of an Operator -- 0.3. Convergence and Stability -- 0.4. Projections and Isometries -- 0.5. Invariant Subspaces -- 0.6. Spectral Theorem -- 1. Equivalence -- 1.1. Parts -- 1.2. Norms -- 2. Shifts -- 2.1. Unilateral Shifts -- 2.2. Bilateral Shifts -- 3. Contractions -- 3.1. The Strong Limits of {T*nTn} and {TnT*n} -- 3.2. The Isometry V on R(A)- -- 4. Quasisimilarity -- 4.1. Invariant Subspaces -- 4.2. Hyperinvariant Subspaces -- 4.3. Contractions Quasisimilar to a Unitary Operator -- 5. Decompositions -- 5.1. Nagy-Foia?—Langer Decomposition -- 5.2. von Neumann-Wold Decomposition -- 5.3. A Decomposition for Contractions with A = A2 -- 6. Models -- 6.1. Rota’s Model -- 6.2. de Branges-Rovnyak Refinement -- 6.3. Durszt Extension -- 7. Applications -- 7.1. A Pattern for Contractions -- 7.2. Foguel Decomposition -- 8. Similarity -- 8.1. Power Boundedness -- 8.2. Weak and Strong Stability -- References
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XII, 132 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461219989
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-1998-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089793
  • (SSID)ssj0001297236
  • (PQKBManifestationID)11743132
  • (PQKBTitleCode)TC0001297236
  • (PQKBWorkID)11363028
  • (PQKB)10513665
  • (DE-He213)978-1-4612-1998-9
  • (MiAaPQ)EBC3076918
  • (EXLCZ)993400000000089793
Label
An Introduction to Models and Decompositions in Operator Theory, by Carlos S. Kubrusly, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
0. Preliminaries -- 0.1. Hilbert-Space Operators -- 0.2. Spectrum of an Operator -- 0.3. Convergence and Stability -- 0.4. Projections and Isometries -- 0.5. Invariant Subspaces -- 0.6. Spectral Theorem -- 1. Equivalence -- 1.1. Parts -- 1.2. Norms -- 2. Shifts -- 2.1. Unilateral Shifts -- 2.2. Bilateral Shifts -- 3. Contractions -- 3.1. The Strong Limits of {T*nTn} and {TnT*n} -- 3.2. The Isometry V on R(A)- -- 4. Quasisimilarity -- 4.1. Invariant Subspaces -- 4.2. Hyperinvariant Subspaces -- 4.3. Contractions Quasisimilar to a Unitary Operator -- 5. Decompositions -- 5.1. Nagy-Foia?—Langer Decomposition -- 5.2. von Neumann-Wold Decomposition -- 5.3. A Decomposition for Contractions with A = A2 -- 6. Models -- 6.1. Rota’s Model -- 6.2. de Branges-Rovnyak Refinement -- 6.3. Durszt Extension -- 7. Applications -- 7.1. A Pattern for Contractions -- 7.2. Foguel Decomposition -- 8. Similarity -- 8.1. Power Boundedness -- 8.2. Weak and Strong Stability -- References
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XII, 132 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461219989
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-1998-9
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089793
  • (SSID)ssj0001297236
  • (PQKBManifestationID)11743132
  • (PQKBTitleCode)TC0001297236
  • (PQKBWorkID)11363028
  • (PQKB)10513665
  • (DE-He213)978-1-4612-1998-9
  • (MiAaPQ)EBC3076918
  • (EXLCZ)993400000000089793

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