Representation of 𝐶ⁿ-operators

Kantorovitz, S.; Pei, K. J.

doi:10.1090/S0002-9939-1975-0367692-2

Representation of $C^{n}$-operators
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by S. Kantorovitz and K. J. Pei PDF

Proc. Amer. Math. Soc. 48 (1975), 152-156 Request permission

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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