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ArticleOriginal scientific text

Title

On the dependence of the orthogonal projector on deformations of the scalar product

Authors 1

Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

Abstract

We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.

Keywords

ENG
scalar product, orthogonal projector, dependence of projectors on scalar products

Bibliography

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Studia Mathematica
1998/128/1
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Pages:
1-17
Main language of publication
English
Received
1996-03-06
Accepted
1997-03-06
Published
1998
Exact and natural sciences