Local polynomials are polynomials
Studia Mathematica, Tome 115 (1995) no. 2, p. 105.

Voir la notice de l'article dans European Digital Mathematics Library

We prove that a function f is a polynomial if G◦f is a polynomial for every bounded linear functional G. We also show that an operator-valued function is a polynomial if it is locally a polynomial.
Classification : 47A05, 47A56, 47A60
Mots-clés : local polynomials, operator-valued function 
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C. Fong; G. Lumer; E. Nordgren; H. Radjavi; P. Rosenthal. Local polynomials are polynomials. Studia Mathematica, Tome 115 (1995) no. 2, p. 105. https://geodesic-test.mathdoc.fr/item/STUMA_1995__115_2_216201/