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The order of neutrality for linear operators on inner product spaces

✍ Scribed by P. Lancaster; A.S. Markus; P. Zizler

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
290 KB
Volume
259
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let A be a symmetric linear operator defined on all of a (possibly degenerate) indefinite inner product space &4 Let JV be the set of all subspaces of 2 which are A-invariant, neutral (in the sense of the indefinite scalar product), and finite dimensional. It is shown that members of JV which are maximal (with respect to inclusion) all have the same dimension. This is called the "order of neutrality" of A and admits immediate application to self-adjoint operators on a Pontrjagin space.

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