The $p$-Banach Saks property in symmetric operator spaces
نویسندگان
چکیده
منابع مشابه
The Banach-saks Property of the Banach Product Spaces
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.
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For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$, it is shown that the strong Banach-Saks-ness of all evaluation operators on ${mathcal M}$ is a sufficient condition for the weak Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in Y^*$, the evaluation op...
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A characterization of Haar null sets in the sense of Christensen is given. Using it, we show that if the dual of a Banach space X has the Banach-Saks property, then closed and convex subsets of X with empty interior are Haar null.
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Let E be a rearrangement-invariant Banach function space on [0, 1], and let Γ(E) denote the set of all p ≥ 1 such that any sequence {xn} in E converging weakly to 0 has a subsequence {yn} with supm m−1/p‖ ∑ 1≤k≤m yn‖ < ∞. The set Γi(E) is defined similarly, but only sequences {xn} of independent random variables are taken into account. It is proved (under the assumption Γ(E) = {1}) that if Γi(E...
متن کاملweak banach-saks property in the space of compact operators
for suitable banach spaces $x$ and $y$ with schauder decompositions and a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$, it is shown that the strong banach-saks-ness of all evaluation operators on ${mathcal m}$ is a sufficient condition for the weak banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in y^*$, the evaluation op...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2007
ISSN: 0019-2082
DOI: 10.1215/ijm/1258138539