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

• Autorzy: Zbigniew Pasternak-Winiarski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

scalar product; orthogonal projector; dependence of projectors on scalar products

Kategorie tematyczne

• 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
• 47B65: Positive operators and order-bounded operators
• 47A55: Perturbation theory
• 46C99: None of the above, but in this section
• 47A62: Equations involving linear operators, with operator unknowns
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 128
• Numer: 1
• Strony: 1-17

Daty

wydano

1998

otrzymano

1996-03-06

poprawiono

1997-03-06

poprawiono

1997-09-22

Twórcy

autor

Zbigniew Pasternak-Winiarski

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

Bibliografia

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