Displaying similar documents to “Again on the weak law in martingale type p Banach spaces.”

Abel means of operator-valued processes

G. Blower (1995)

Studia Mathematica

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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.

Clarkson type inequalities and their relations to the concepts of type and cotype.

Mikio Kato, Lars-Erik. Persson, Yasuji Takahashi (2000)

Collectanea Mathematica

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We prove some multi-dimensional Clarkson type inequalities for Banach spaces. The exact relations between such inequalities and the concepts of type and cotype are shown, which gives a conclusion in an extended setting to M. Milman's observation on Clarkson's inequalities and type. A similar investigation conceming the close connection between random Clarkson inequality and the corresponding concepts of type and cotype is also included. The obtained results complement, unify and generalize...