Lie Algebras of Bounded Operators: 120 (Operator Theory: Advances and Applications) - Softcover

Beltita, Daniel; Sabac, Mihai

Softcover

ISBN 10: 3034895208 ISBN 13: 9783034895200

Verlag: Birkhäuser, 2012

Inhaltsangabe

In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi­ trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.

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Reseña del editor

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 3034895208
• ISBN 13: 9783034895200
• Einband: Tapa blanda
• Anzahl der Seiten: 232
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar