Hilbert Space Operators: A Problem Solving Approach

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Birkhäuser, Jan 1, 2003 - Hilbert space - 149 pages
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This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.

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Contents

Invariant Subspaces
1
Hilbert Space Operators
13
Convergence and Stability
23
Reducing Subspaces
33
Shifts
41
Decompositions
51
Hyponormal Operators
65
Spectral Properties
75
Paranormal Operators
93
Proper Contractions
109
Quasireducible Operators
117
The Lomonosov Theorem
129
References
143
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