Abstract
We construct the functional calculus for full operators with discrete spectrum over Banach spaces in the interpolation classes of symbols associated with given operators. We describe new classes of full operators in Banach spaces.
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Literature Cited
I. M. Glazman and Yu. I. Lyubich,Finite-Dimensional Linear Analysis [in Russian], Nauka, Moscow (1969)
N. Dunford and J. T. Schwartz,Linear Operators. Spectral Theory, Interscience, New York (1958).
T. Kato,Theory of Perturbations of Linear Operators [Russian translation], Mir, Moscow (1972).
O. V. Lopushans'kyi, “Locally convex operators III. Functional calculus on semiregular spectra,” Preprint, Ukrainian Academy of Sciences Institute for Applied Problems, of Mechanics and Mathematics, L'viv (1993).
O. V. Lopushans'kyi, “The operator calculus on ultrasmooth vectors,”Ukr. Mat. Zh.,44, No. 4, 502–513 (1992).
H. Triebel,Theory of Interpolations, Functional Spaces, and Differential Operators [Russian translation], Mir, Moscow (1980).
H. Tanabe,Equations of Evolution, Pitman, London (1979).
Additional information
Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998 pp. 127–135.
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Lopushans'kyi, O.V., Dmytryshyn, M.I. The functional calculus of full operators with discrete spectrum. J Math Sci 97, 3872–3878 (1999). https://doi.org/10.1007/BF02364927
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DOI: https://doi.org/10.1007/BF02364927