Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
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
Czasopismo
Rocznik
Tom
Numer
Strony
1-17
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-03-06
poprawiono
1997-03-06
poprawiono
1997-09-22
Twórcy
- Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland, pastwin@alpha.im.pw.edu.pl
Bibliografia
- [1] S. Bergman, The Kernel Function and Conformal Mapping, Math. Surveys Monographs 5, Amer. Math. Soc., 2nd rev. ed., 1970.
- [2] S. G. Krantz, Function Theory of Several Complex Variables, Interscience-Wiley, New York, 1982.
- [3] J.-P. Labrousse, The general local form of an analytic mapping into the set of idempotent elements of a Banach algebra, Proc. Amer. Math. Soc. 123 (1995), 3467-3471.
- [4] A. Odzijewicz, On reproducing kernels and quantization of states, Comm. Math. Phys. 114 (1988), 577-597.
- [5] A. Odzijewicz, Coherent states and geometric quantization, ibid. 150 (1992), 385-413.
- [6] K. Maurin, Analysis, Part I, Elements, PWN-Reidel, Warszawa-Dordrecht, 1976.
- [7] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134.
- [8] Z. Pasternak-Winiarski, On reproducing kernels for holomorphic vector bundles, in: Quantization and Infinite-Dimensional Systems, J.-P. Antoine, S. Twareque Ali, W. Lisiecki, I. M. Mladenov and A. Odzijewicz (eds.), Plenum Press, New York, 1994, 109-112.
- [9] Z. Pasternak-Winiarski, Bergman spaces and kernels for holomorphic vector bundles, Demonstratio Math. 30 (1997), 199-214.
- [10] J. H. Rawnsley, Coherent states and Kähler manifolds, Quart. J. Math. Oxford Ser. 28 (1077), 403-415.
- [11] K. Yosida, Functional Analysis, Springer, Berlin, 1965.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv128i1p1bwm