Overview
- Authors:
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Daniel Beltiţă
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Institute of Mathematics, “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
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Mihai Şabac
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Faculty of Mathematics, University of Bucharest, Bucharest, Romania
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Table of contents (5 chapters)
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Front Matter
Pages i-viii
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- Daniel Beltiţă, Mihai Şabac
Pages 1-79
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- Daniel Beltiţă, Mihai Şabac
Pages 81-102
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- Daniel Beltiţă, Mihai Şabac
Pages 103-132
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- Daniel Beltiţă, Mihai Şabac
Pages 133-180
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- Daniel Beltiţă, Mihai Şabac
Pages 181-202
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Back Matter
Pages 203-219
About this book
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.
Authors and Affiliations
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Institute of Mathematics, “Simion Stoilow” of the Romanian Academy, Bucharest, Romania
Daniel Beltiţă
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Faculty of Mathematics, University of Bucharest, Bucharest, Romania
Mihai Şabac
