Book Review: Indefinite inner product spaces
نویسندگان
چکیده
منابع مشابه
Normal Matrices in Degenerate Indefinite Inner Product Spaces
Complex matrices that are structured with respect to a possibly degenerate indefinite inner product are studied. Based on the theory of linear relations, the notion of an adjoint is introduced: the adjoint of a matrix is defined as a linear relation which is a matrix if and only if the inner product is nondegenerate. This notion is then used to give alternative definitions of selfadjoint and un...
متن کاملEla Shells of Matrices in Indefinite Inner Product Spaces
The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...
متن کاملCanonical matrices of isometric operators on indefinite inner product spaces
We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay) = B(x, y) on a vector space over F in the following cases: • F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; • F is an algebraically closed field of characteristic 0 or the skew field of qu...
متن کامل$C^{*}$-semi-inner product spaces
In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.
متن کاملShells of matrices in indefinite inner product spaces
The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13892-4