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Triangular and Jordan Representations of Linear Operators
M. S. Brodskii

Translations of Mathematical Monographs
1971; 246 pp; softcover
Volume: 32
ISBN-10: 0-8218-4163-7
ISBN-13: 978-0-8218-4163-1
List Price: US$88
Member Price: US$70.40
Order Code: MMONO/32.S
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Determining the invariant subspaces of any given transformation and writing the transformation as an integral in terms of invariant subspaces is a fundamental problem. This book presents the foundations of the theory of triangular and Jordan representations of bounded linear operators in Hilbert space and solves the problem in the case of completely continuous transformations. The reader is assumed to know the basics of linear operator theory.


Graduate students and research mathematicians interested in analysis.

Table of Contents

  • Operator and matrix nodes. Characteristic functions of nodes
  • Triangular representations of Volterra operators and multiplicative representations of characteristic functions of Volterra nodes
  • Unicellular operators. Jordan representations of dissipative Volterra operators with nuclear imaginary components
  • Appendix I. Generalization of Naĭmark's theorem
  • Invertible holomorphic operator-functions
  • Notes on the literature and additional remarks
  • Bibliography
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