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Representation of $ C\sp{n}$-operators


Authors: S. Kantorovitz and K. J. Pei
Journal: Proc. Amer. Math. Soc. 48 (1975), 152-156
MSC: Primary 47A60
DOI: https://doi.org/10.1090/S0002-9939-1975-0367692-2
MathSciNet review: 0367692
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Abstract: The operator $ {T_n} = M + nJ$ acting in $ C(I)$, where $ I = [0,1],M:f(x) \to xf(x)$, and $ J:f(x) \to \int_0^x {f(t)} dt$, is known to be of class $ {C^n}$ (cf. [2], [3], [4]). We show here that every real operator of class $ {C^n}$ in a weakly complete Banach space $ X$ has a ``weak representation'' as $ {T_n}$.


References [Enhancements On Off] (What's this?)

  • [1] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [2] S. Kantorovitz, Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc. 115 (1965), 194-224. MR 33 #7855. MR 0199712 (33:7855)
  • [3] -, The $ {C^k}$-classification of certain operators in $ {L_p}$, Trans. Amer. Math. Soc. 132 (1968), 323-333. MR 37 #2033. MR 0226443 (37:2033)
  • [4] -, The $ {C^k}$-classification of certain operators in $ {L_p}$. II, Trans. Amer. Math. Soc. 146 (1969), 61-67. MR 40 #4814. MR 0251587 (40:4814)
  • [5] B. Walsh, Spectral decomposition of quasi-Montel spaces, Proc. Amer. Math. Soc. 17 (1966), 1267-1271. MR 34 #4914. MR 0205079 (34:4914)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0367692-2
Keywords: $ {C^n}$-operators, representation, operator measure, characteristic operator
Article copyright: © Copyright 1975 American Mathematical Society

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