Abel means of operator-valued processes

G. Blower

Studia Mathematica (1995)

  • Volume: 115, Issue: 3, page 261-276
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Blower, G.. "Abel means of operator-valued processes." Studia Mathematica 115.3 (1995): 261-276. <http://eudml.org/doc/216212>.

@article{Blower1995,
abstract = {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.},
author = {Blower, G.},
journal = {Studia Mathematica},
keywords = {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},
language = {eng},
number = {3},
pages = {261-276},
title = {Abel means of operator-valued processes},
url = {http://eudml.org/doc/216212},
volume = {115},
year = {1995},
}

TY - JOUR
AU - Blower, G.
TI - Abel means of operator-valued processes
JO - Studia Mathematica
PY - 1995
VL - 115
IS - 3
SP - 261
EP - 276
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/216212
ER -

References

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