Abel means of operator-valued processes
Studia Mathematica, Tome 115 (1995) no. 3, p. 261.

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

Let ( X j ) be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of X n . . . X 2 X 1 to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.
Classification : 60G46, 47B80
Mots-clés : Abel means, martingale transforms, subadditive ergodic theory, sequence of independent identically distributed random operators on a Banach space, Hardy and Lipschitz spaces, Fourier coefficients of random Taylor series with bounded martingale coefficients, Lipschitz and Bergman spaces 
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G. Blower. Abel means of operator-valued processes. Studia Mathematica, Tome 115 (1995) no. 3, p. 261. https://geodesic-test.mathdoc.fr/item/STUMA_1995__115_3_216212/