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Spectral theory of block operator matrices and applications. (English) Zbl 1173.47003

London: Imperial College Press (ISBN 978-1-86094-768-1/hbk; 978-1-84816-112-2/ebook). xxxi, 264 p. (2008).
Block operator matrices are matrices in which the elements are linear operators between Banach or Hilbert spaces. They occur in various branches of mathematics and its applications, such as in the theory of Hamiltonians, the discretization of partial differential equations, saddle point problems in nonlinear analysis and in some aspects of fluid mechanics.
In the book under review, particular emphasis is placed on classes of block operator matrices to which standard operator theoretical methods do not apply, and the main topics include localization of the spectrum, investigation of the essential spectrum, variational principles, block diagonalization and invariant subspaces, solutions of algebraic Riccati equations and various aspects of fluid dynamics and quantum mechanics.

MSC:

47A10 Spectrum, resolvent
76W05 Magnetohydrodynamics and electrohydrodynamics
35A99 General topics in partial differential equations
47-02 Research exposition (monographs, survey articles) pertaining to operator theory

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