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The Resource Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource)
Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource)
Resource Information
The item Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 There is a fruitful and fascinating interaction between infinite dimensional operator theory (particularly decomposable, scalar and spectral generalized operator theory due to C. Foias and I. Colojoara) and Lie algebra theory. The present book is the first devoted to this field, ranging from some short historical notes to the most recent developments. Nilpotence criteria, infinite dimensional variants of Lie's theorem for solvable systems of bounded operators, spectral properties of elements of semisimple Lie algebras and simultaneous triangularisation are expounded. The book is selfcontained and features an extensive bibliography. It is aimed at postgraduate students and researchers who are introduced to an interesting recent area of research and will learn some new methods useful for both of the domains  operator theory and Lie algebra theory
 Language
 eng
 Extent
 1 online resource (VIII, 219 pages).
 Contents

 I Preliminaries
 A Lie Algebras
 B Complexes
 C Spectral Theory in Complex Banach Space
 II The Commutators and Nilpotence Criteria
 ʹ 15 An asymptotic formula for the commutators
 ʹ 16 Nilpotence criteria in an associative algebra
 ʹ 17 Quasinilpotence and nilpotence criteria in complex Banach algebras
 ʹ 18 Nilpotent elements in LMdecomposable Lie subalgebras of an associative algebra
 ʹ 19 Nilpotent elements in LMdecomposable Lie algebras of bounded linear operators
 Notes
 III Infinitedimensional Variants of the Lie and Engel Theorems
 ʹ 20 Weights for operator algebras
 ʹ 21 Invariant subspaces for LMdecomposable Lie algebras of bounded operators
 ʹ 22 The irreducible representations of an LMdecomposable Lie algebra. Infinitedimensional variant of Lie's Theorem on a complex Banach space
 ʹ 23 The associative envelope of a Lie algebra of quasinilpotent operators
 ʹ 24 Commutativity modulo the Jacobson radical
 Notes
 IV Spectral Theory for Solvable Lie Algebras of Operators
 ʹ 25 Spectral theory for representations of Lie algebras
 ʹ 26 Spectral theory for systems of operators generating nilpotent Lie algebras
 ʹ 27 The CartanTaylor spectrum of a locally solvable Lie algebra of operators
 ʹ 28 Lie ideals of generalized spectral operators
 Notes
 V Semisimple Lie Algebras of Operators
 ʹ 29 Lie subalgebra with involution consisting of bounded operators on a complex Banach space. Normal elements given by a space of selfadjoint operators
 ʹ 30 Individual spectral properties in ideally finite semisimple Lie algebras of operators
 ʹ 31 Semisimple Lie algebras of compact quasinilpotent operators
 Notes
 List of Symbols
 Isbn
 9783034883320
 Label
 Lie Algebras of Bounded Operators
 Title
 Lie Algebras of Bounded Operators
 Statement of responsibility
 by Daniel Beltiţă, Mihai Şabac
 Language
 eng
 Summary
 There is a fruitful and fascinating interaction between infinite dimensional operator theory (particularly decomposable, scalar and spectral generalized operator theory due to C. Foias and I. Colojoara) and Lie algebra theory. The present book is the first devoted to this field, ranging from some short historical notes to the most recent developments. Nilpotence criteria, infinite dimensional variants of Lie's theorem for solvable systems of bounded operators, spectral properties of elements of semisimple Lie algebras and simultaneous triangularisation are expounded. The book is selfcontained and features an extensive bibliography. It is aimed at postgraduate students and researchers who are introduced to an interesting recent area of research and will learn some new methods useful for both of the domains  operator theory and Lie algebra theory
 Cataloging source
 I9W
 http://library.link/vocab/creatorName
 Beltiţă, Daniel
 Dewey number
 510
 Index
 no index present
 LC call number
 QA1939
 Literary form
 non fiction
 Nature of contents
 encyclopedias
 http://library.link/vocab/relatedWorkOrContributorName
 Şabac, Mihai
 Series statement
 Operator Theory: Advances and Applications
 Series volume
 120
 http://library.link/vocab/subjectName

 Mathematics
 Mathematics
 Label
 Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 I Preliminaries  A Lie Algebras  B Complexes  C Spectral Theory in Complex Banach Space  II The Commutators and Nilpotence Criteria  ʹ 15 An asymptotic formula for the commutators  ʹ 16 Nilpotence criteria in an associative algebra  ʹ 17 Quasinilpotence and nilpotence criteria in complex Banach algebras  ʹ 18 Nilpotent elements in LMdecomposable Lie subalgebras of an associative algebra  ʹ 19 Nilpotent elements in LMdecomposable Lie algebras of bounded linear operators  Notes  III Infinitedimensional Variants of the Lie and Engel Theorems  ʹ 20 Weights for operator algebras  ʹ 21 Invariant subspaces for LMdecomposable Lie algebras of bounded operators  ʹ 22 The irreducible representations of an LMdecomposable Lie algebra. Infinitedimensional variant of Lie's Theorem on a complex Banach space  ʹ 23 The associative envelope of a Lie algebra of quasinilpotent operators  ʹ 24 Commutativity modulo the Jacobson radical  Notes  IV Spectral Theory for Solvable Lie Algebras of Operators  ʹ 25 Spectral theory for representations of Lie algebras  ʹ 26 Spectral theory for systems of operators generating nilpotent Lie algebras  ʹ 27 The CartanTaylor spectrum of a locally solvable Lie algebra of operators  ʹ 28 Lie ideals of generalized spectral operators  Notes  V Semisimple Lie Algebras of Operators  ʹ 29 Lie subalgebra with involution consisting of bounded operators on a complex Banach space. Normal elements given by a space of selfadjoint operators  ʹ 30 Individual spectral properties in ideally finite semisimple Lie algebras of operators  ʹ 31 Semisimple Lie algebras of compact quasinilpotent operators  Notes  List of Symbols
 Dimensions
 unknown
 Extent
 1 online resource (VIII, 219 pages).
 Form of item
 online
 Isbn
 9783034883320
 Isbn Type
 (electronic bk.)
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783034883320
 Specific material designation
 remote
 System control number

 (OCoLC)840290502
 (OCoLC)ocn840290502
 Label
 Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource)
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 I Preliminaries  A Lie Algebras  B Complexes  C Spectral Theory in Complex Banach Space  II The Commutators and Nilpotence Criteria  ʹ 15 An asymptotic formula for the commutators  ʹ 16 Nilpotence criteria in an associative algebra  ʹ 17 Quasinilpotence and nilpotence criteria in complex Banach algebras  ʹ 18 Nilpotent elements in LMdecomposable Lie subalgebras of an associative algebra  ʹ 19 Nilpotent elements in LMdecomposable Lie algebras of bounded linear operators  Notes  III Infinitedimensional Variants of the Lie and Engel Theorems  ʹ 20 Weights for operator algebras  ʹ 21 Invariant subspaces for LMdecomposable Lie algebras of bounded operators  ʹ 22 The irreducible representations of an LMdecomposable Lie algebra. Infinitedimensional variant of Lie's Theorem on a complex Banach space  ʹ 23 The associative envelope of a Lie algebra of quasinilpotent operators  ʹ 24 Commutativity modulo the Jacobson radical  Notes  IV Spectral Theory for Solvable Lie Algebras of Operators  ʹ 25 Spectral theory for representations of Lie algebras  ʹ 26 Spectral theory for systems of operators generating nilpotent Lie algebras  ʹ 27 The CartanTaylor spectrum of a locally solvable Lie algebra of operators  ʹ 28 Lie ideals of generalized spectral operators  Notes  V Semisimple Lie Algebras of Operators  ʹ 29 Lie subalgebra with involution consisting of bounded operators on a complex Banach space. Normal elements given by a space of selfadjoint operators  ʹ 30 Individual spectral properties in ideally finite semisimple Lie algebras of operators  ʹ 31 Semisimple Lie algebras of compact quasinilpotent operators  Notes  List of Symbols
 Dimensions
 unknown
 Extent
 1 online resource (VIII, 219 pages).
 Form of item
 online
 Isbn
 9783034883320
 Isbn Type
 (electronic bk.)
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783034883320
 Specific material designation
 remote
 System control number

 (OCoLC)840290502
 (OCoLC)ocn840290502
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