# Abel means of operator-valued processes

Studia Mathematica (1995)

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

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topBlower, 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

top- [1] G. R. Allan, A. G. O'Farrell and T. J. Ransford, A tauberian theorem arising in operator theory, Bull. London Math. Soc. 19 (1987), 537-545. Zbl0652.46041
- [2] O. Blasco, Spaces of vector valued analytic functions and applications, in: Geometry of Banach Space, P. F. X. Müller and W. Schachermayer (eds.), London Math. Soc. Lecture Note Ser. 158, Cambridge Univ. Press, 1990, 33-48. Zbl0736.46024
- [3] O. Blasco and A. Pełczyński, Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces, Trans. Amer. Math. Soc. 323 (1991), 335-367. Zbl0744.46039
- [4] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge Univ. Press, 1973. Zbl0262.47001
- [5] J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Mat. 21 (1983), 163-168. Zbl0533.46008
- [6] D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in: Conference on Harmonic Analysis in Honor of Antoni Zygmund, W. Beckner et al. (eds.), Wadsworth, Belmont, Calif., 1983, 270-286.
- [7] G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), 403-439. Zbl0003.15601
- [8] J. Jakubowski and S. Kwapień, On multiplicative systems of functions, Bull. Acad. Polon. Sci. 27 (1979), 689-694. Zbl0493.42036
- [9] J. P. Kahane, Some Random Series of Functions, 2nd ed., Cambridge, 1985. Zbl0571.60002
- [10] Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 313-328. Zbl0611.47005
- [11] J. F. C. Kingman, Subadditive ergodic theory, Ann. Probab. 1 (1973), 883-909. Zbl0311.60018
- [12] D. Ornstein and L. Sucheston, An operator theorem on ${L}_{1}$ convergence to zero with applications to Markov kernels, Ann. Math. Statist. 41 (1970), 1631-1639. Zbl0284.60068
- [13] G. C. Rota, On the maximal ergodic theorem for Abel limits, Proc. Amer. Math. Soc. 14 (1963), 722-723. Zbl0117.10501
- [14] N. Th. Varopoulos, Isoperimetric inequalities and Markov chains, J. Funct. Anal. 63 (1985), 215-239. Zbl0573.60059

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