Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

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Gesztesy, Fritz; Malamud, Mark; Mitrea, Marius; Naboko, Serguei;
(2008)
  • Subject: 47A05, 47A07, 47A55 | Mathematics - Spectral Theory | Mathematics - Functional Analysis
    arxiv: Mathematics::Spectral Theory

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.
  • References (21)
    21 references, page 1 of 3

    [1] Ju. L. Dalecki˘ı and M. G. Kre˘ın, Stability of Solutions of Differential Equations in Banach Space, Transl. Math. Monographs, 43, Amer. Math. Soc., Providence, RI, 1974.

    [2] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Wiley-Interscience, New York, 1988.

    [3] N. Dunford and J. T. Schwartz, Linear Operators, Part III: Spectral Operators, Wiley-Interscience, New York, 1988.

    [4] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1989.

    [5] B. Fuglede, A commutativity theorem for normal operators, Proc. Nat. Acad. Sci., USA, 33, 35-40 (1950).

    [6] T. Kato, A generalization of the Heinz inequality, Proc. Japan Acad. 37, 305-308 (1961).

    [7] T. Kato, Fractional powers of dissipative operators, J. Math. Soc. Japan, 13, 246-274 (1961).

    [8] T. Kato, Fractional powers of dissipative operators, II, J. Math. Soc. Japan, 14, 242-248 (1962).

    [9] T. Kato, Perturbation Theory for Linear Operators, corr. printing of the 2nd ed., Springer, Berlin, 1980.

    [10] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, and P. E. Sobolevskii, Integral Operators in Spaces of Summable Functions, Noordhoff, Leyden, 1976.

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