Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dilation of Ritt operators on L^{p}-spaces   For any Ritt operator T:L^{p}(\Omega) --> L^{p}(\Omega), for any positive
real number \alpha, and for any x in L^{p}, we consider the square functions |x
|_{T,\alpha} = \Bigl| \Bigl(\sum_{k=1}^{\infty} k^{2\alpha -1}\bigl
|T^{k-1}(I-T)^\alpha x \bigr|^2 \Bigr)^{1/2}_{L^{p}}. We show that if T is
actually an R-Ritt operator, then these square functions are pairwise
equivalent. Then we show that T and its adjoint T* acting on L^{p'} both
satisfy uniform estimates |x|_{T,1} \lesssim |x|_{L^{p}} and |y|_{T*,1}
\lesssim |y|_{L^{p'}} for x in L^{p} and y in L^{p'} if and only if T is R-Ritt
and admits a dilation in the following sense: there exist a measure space
\widetilde{\Omega}, an isomorphism U of L^{p}(\widetilde{\Omega}) such that the
sequence of all U^{n} for n varying in Z is bounded, as well as two bounded
maps J : L^{p}(\Omega) --> L^{p}(\widetilde{\Omega}) and Q :
L^{p}(\widetilde{\Omega}) --> L^p(\Omega) such that T^{n}=QU^{n}J for any
nonnegative integer n. We also investigate functional calculus properties of
Ritt operators and analogs of the above results on noncommutative L^{p}-spaces.

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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph