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)

Label
Lie Algebras of Bounded Operators
Title
Lie Algebras of Bounded Operators
Statement of responsibility
by Daniel Beltiţă, Mihai Şabac
Creator
Contributor
Subject
Genre
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 self-contained 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
Member of
Cataloging source
I9W
http://library.link/vocab/creatorName
Beltiţă, Daniel
Dewey number
510
Index
no index present
LC call number
QA1-939
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)
Link
http://dx.doi.org/10.1007/978-3-0348-8332-0
Instantiates
Publication
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 LM-decomposable Lie subalgebras of an associative algebra -- ʹ 19 Nilpotent elements in LM-decomposable Lie algebras of bounded linear operators -- Notes -- III Infinite-dimensional Variants of the Lie and Engel Theorems -- ʹ 20 Weights for operator algebras -- ʹ 21 Invariant subspaces for LM-decomposable Lie algebras of bounded operators -- ʹ 22 The irreducible representations of an LM-decomposable Lie algebra. Infinite-dimensional 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 Cartan-Taylor 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 self-adjoint 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
10.1007/978-3-0348-8332-0
Specific material designation
remote
System control number
  • (OCoLC)840290502
  • (OCoLC)ocn840290502
Label
Lie Algebras of Bounded Operators, by Daniel Beltiţă, Mihai Şabac, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-0348-8332-0
Publication
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 LM-decomposable Lie subalgebras of an associative algebra -- ʹ 19 Nilpotent elements in LM-decomposable Lie algebras of bounded linear operators -- Notes -- III Infinite-dimensional Variants of the Lie and Engel Theorems -- ʹ 20 Weights for operator algebras -- ʹ 21 Invariant subspaces for LM-decomposable Lie algebras of bounded operators -- ʹ 22 The irreducible representations of an LM-decomposable Lie algebra. Infinite-dimensional 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 Cartan-Taylor 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 self-adjoint 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
10.1007/978-3-0348-8332-0
Specific material designation
remote
System control number
  • (OCoLC)840290502
  • (OCoLC)ocn840290502

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