Daniel Beltita's Books

Lie Algebras of Bounded Operators

By: Daniel Beltita,Mihai Sabac

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Lie Algebras of Bounded Operators

By: Daniel Beltita,Mihai Sabac

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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Page Count

226

Publisher

Birkhäuser

Published Date

ISBN 10

3034883323

ISBN 13

9783034883320

Smooth Homogeneous Structures in Operator Theory

By: Daniel Beltita

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Smooth Homogeneous Structures in Operator Theory

By: Daniel Beltita

Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research. Requiring only a moderate familiarity with funct

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Page Count

319

Publisher

CRC Press

Published Date

ISBN 10

1420034804

ISBN 13

9781420034806

The State Space Method

Generalizations and Applications

By: Daniel Alpay,Israel Gohberg

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The State Space Method

Generalizations and Applications

By: Daniel Alpay,Israel Gohberg

The state space method developed in the last decades allows us to study the theory of linear systems by using tools from the theory of linear operators; conversely, it had a strong influence on operator theory introducing new questions and topics. The present volume contains a collection of essays representing some of the recent advances in the state space method. Methods covered include noncommutative systems theory, new aspects of the theory of discrete systems, discrete analogs of canonical systems, and new applications to the theory of Bezoutiants and convolution equations. The articles in the volume will be of interest to pure and applied mathematicians, electrical engineers and theoretical physicists.

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