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Indefinite inner product spaces.

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Published by Springer in Berlin, New York .
Written in English


  • Indefinite inner product spaces.

Book details:

Edition Notes

Bibliography: p. [210]-220.

SeriesErgebnisse der Mathematik und ihrer Grenzgebiete,, Bd. 78
LC ClassificationsQA322.5 .B63
The Physical Object
Paginationix, 223 p.
Number of Pages223
ID Numbers
Open LibraryOL5418243M
ISBN 100387062025
LC Control Number73010669

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Indefinite Inner Product Spaces. Authors: Bognar, J. Free Preview. Buy this book eB89 Linear Operators in Inner Product Spaces without Topology. Pages Bognár, János. Book Title Indefinite Inner Product Spaces Authors. J. Bognar; Series Title.   Description By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi- tian) bilinear form prescribed on it so . By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi- tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. Part of the Operator Theory: Advances and Applications book series (OT, volume ) Also part of the Linear Operators and Linear Systems book sub series (LOLS, volume ) Heinz Langer – Pioneer of Operator Theory in Indefinite Inner Product Spaces. Bernd Kirstein.

Inner products and the metric operator. Consider a complex vector space equipped with an indefinite hermitian form ⋅, ⋅.In the theory of Krein spaces it is common to call such an hermitian form an indefinite inner following subsets are defined in terms of the square norm induced by the indefinite inner product: = {∈: =} ("neutral"). Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. A colloquium on operator theory was held in Vienna, Austria, in March , on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with.   A vector space V with an indefinite inner product is an indefinite inner product space, see,. Let us consider the n-dimensional vector space C n with an indefinite inner product structure induced by the Minkowski inner product (1) [x, y] J = y ∗ J x, x, y ∈ C n, where J = diag (− 1, 1, , 1) is the metric matrix. We say that x, y are.

Keywords: Indefinite matrix product, indefinite inner product spaces, commutators AMS Mathematics Subject Classification (): 46C20, 15A09 1. Introduction An indefinite inner product in is a conjugate symmetric sesquilinear form (,) together with the regularity condition that (,)=0 for all ∈ only when =0. There are indefinite scalar product spaces. I suggest reading "Indefinite Linear Algebra and Applications" by Gohberg, Lancaster, ations are wide; to name a few: theory of relativity and the research of polarized light (mostly Minkowski space is used here), and matrix polynomials (nicely covered in "Matrix polynomials", again by Gohberg, Lancaster, Rodman). -space. A pair of objects, the first of which is a vector space over the field of complex numbers, while the second is a bilinear (more precisely, sesquilinear) form on ; this form is also called a is a positive-definite (a so-called definite) form, then it is a scalar product in, and one can use it to canonically introduce (cf., e.g., Hilbert space with an indefinite metric) a. Daniel Alpay, "Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations: A Volume Dedicated to Heinz Langer" English | ISBN: | | pages | PDF | 22 MB.