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H. Samea 《Mathematica Slovaca》2014,64(4):871-878
In this paper, some relations between L p -spaces on locally compact groups are found. Applying these results proves that for a locally compact group G, the convolution Banach algebras L p (G) ∩ L 1(G) (1 < p ≤ ∞), and A p (G) ∩ L 1(G) (1 < p < ∞) are amenable if and only if G is discrete and amenable. 相似文献
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A notion of Gaussian hemigroup is introduced and its relationship with the Gauss condition is studied. Moreover, a Lévy-type
martingale characterization is proved for processes with independent (not necessarily stationary) increments satisfying the
Gauss condition in a compact Lie group. The characterization is given in terms of a faithful finite dimensional representation
of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups
associated with the increment processes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Monatshefte für Mathematik - Let G be a locally compact abelian group. In this paper, we study derivations on the Banach algebra $$L_0^\infty (G)^*$$ . We prove that any derivation on... 相似文献
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S. G. Dani 《印度理论与应用数学杂志》2010,41(1):241-250
We discuss some properties of nilpotent Lie groups and their application in proving the embedding theorem for infinitely divisible
probability measures on locally compact groups. 相似文献
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For any Ritt operator T: L p (Ω) → L p (Ω), for any positive real number α, and for any x ∈ L p (Ω), we consider $${\left\| x \right\|_{T,\alpha }} = {\left\| {{{\left( {\sum\limits_{k = 1}^\infty {{k^{2\alpha - 1}}} {{\left| {{T^{k - 1}}{{(I - T)}^\alpha }x} \right|}^2}} \right)}^{\frac{1}{2}}}} \right\|_{{L^p}}}$$ . We show that if T is actually an R-Ritt operator, then the square functions \({\left\| {} \right\|_{T,\alpha }}\) are pairwise equivalent. Then we show that T and its adjoint T*: L p′ (Ω) → L p′ (Ω) both satisfy uniform estimates \({\left\| x \right\|_{T,1}} \leqslant {\left\| x \right\|_{{L^p}}}\) and \({\left\| y \right\|_{T*,1}} \leqslant {\left\| y \right\|_{{L^{p'}}}}\) for x ∈ L p (Ω) and y ∈ L p′ (Ω) if and only if T is R-Ritt and admits a dilation in the following sense: there exist a measure space \(\tilde \Omega \) , an isomorphism \(U:{L^p}\tilde \Omega \to {L^p}\tilde \Omega \) such that {U n : n ∈ ?} is bounded, as well as two bounded maps \({L^p}(\Omega )\buildrel J \over \longrightarrow {L^p}(\tilde \Omega )\buildrel Q \over \longrightarrow {L^p}(\Omega )\) such that T n = QU n J for any n ≥ 0. We also investigate functional calculus properties of Ritt operators and analogs of the above results on noncommutative L p -spaces. 相似文献
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S. S. Akbarov 《Mathematical Notes》1992,52(4):995-1002
Translated from Matematicheskie Zametki, Vol. 52, No. 4, pp. 3–14, October, 1992. 相似文献
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L. Tzafriri 《Israel Journal of Mathematics》1969,7(1):9-15
The aim of this note is to study the structure of the range of a contractive projection in a non-separableL
p
-space; 1≦p<+∞.
Supported by National Science Foundation Grant GP-7475 相似文献
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V. G. Pestov 《Ukrainian Mathematical Journal》1988,40(1):109-111
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 1, pp. 127–129, Janaury–February, 1988. 相似文献
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Rodney Nillsen 《Journal of Functional Analysis》1985,64(3):338-357
Let G be a σ-compact and locally compact group. If f?L∞(G) let Uf be the closed subspace of L∞(G) generated by the left translations of f. Conditions are given which ensure that each function in Uf may be expanded in an essentially unique way as an absolutely convergent series of translations of f. In this case Uf contains subspaces which are isometrically isomorphic to l1. If G is metrizable and nondiscrete there is a continuum Γ in L∞(G) such that, for each f?Γ, Uf contains no non-zero continuous function, and for f, g?Γ with f ≠ g, Uf ∩ Ug = {0}. If G is non-compact, metrizable, and non-discrete there is a continuum Γ of bounded continuous functions on G such that, for each f?Γ, Uf contains no non-zero left uniformly continuous function, and for f, g?Γ with f ≠ g, Uf ∩ Ug = {0}. The subspaces Uf above are translation invariant but are not convolution invariant. 相似文献