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.
@article{bwmeta1.element.bwnjournal-article-smv128i1p1bwm,
author = {Zbigniew Pasternak-Winiarski},
title = {On the dependence of the orthogonal projector on deformations of the scalar product},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {1-17},
zbl = {0910.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv128i1p1bwm}
}
Pasternak-Winiarski, Zbigniew. On the dependence of the orthogonal projector on deformations of the scalar product. Studia Mathematica, Tome 129 (1998) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv128i1p1bwm/
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