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Proceedings of the American Mathematical Society

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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
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}$.


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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