Generalized pseudo-hermitian operators
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- by Brian Kritt PDF
- Proc. Amer. Math. Soc. 30 (1971), 343-348 Request permission
Abstract:
An operator in a Banach space is called generalized pseudo-hermitian if it is a generalized scalar in the sense of Foiaş (i.e., admits a spectral distribution) and has a real spectrum. In this paper this class of operators is characterized by the condition that the real exponential group generated by such an operator has polynomial growth in the uniform operator norm.References
- Ciprian Foiaş, Une application des distributions vectorielles à la théorie spectrale, Bull. Sci. Math. (2) 84 (1960), 147–158 (French). MR 123193 L. Hörmander, Linear partial differential operators, Die Grundlehren der math. Wissenschaften, Band 116, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #4221.
- Shmuel Kantorovitz, On the characterization of spectral operators, Trans. Amer. Math. Soc. 111 (1964), 152–181. MR 160115, DOI 10.1090/S0002-9947-1964-0160115-5
- B. Kritt, Spectral decomposition of positive and positive-definite distributions of operators, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 865–870. MR 241972
- Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 343-348
- MSC: Primary 47.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281046-5
- MathSciNet review: 0281046