9783764364045 - lie algebras of bounded operators von beltita, daniel; sabac, mihai (3 Ergebnisse)
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Zustand: New. Expounds 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. This book is suitable for postgraduate students and researchers. Series: Operator Theory: Advances an…d Applications. Num Pages: 227 pages, biography. BIC Classification: PBF; PBKF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 14. Weight in Grams: 509. . 2001. 2001st Edition. hardcover. . . . . Books ship from the US and Ireland.
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, Foiadecomposable, 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.
