On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space
نویسندگان
چکیده
In this paper, numerical ranges associated to operators on an indefinite inner product space are investigated. Boundary generating curves, corners, shapes and computer generations of these sets are studied. In particular, the MurnaghanKippenhahn theorem for the classical numerical range is generalized.
منابع مشابه
Remarks on generalized numerical ranges of operators on indefinite inner product spaces
Numerical ranges associated to operators on an indefinite inner product space are investigated. Boundary generating curves, shapes, corners and computer generation of these sets are studied. Some final remarks present an interesting relation between these sets and numerical ranges of operators arising in quantum mechanics.
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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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تاریخ انتشار 2003