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• W2103014598 abstract "We characterize those classes $ccc$ of separable Banach spaces admitting a separable universal space $Y$ (that is, a space $Y$ containing, up to isomorphism, all members of $ccc$) which is not universal for all separable Banach spaces. The characterization is a byproduct of the fact, proved in the paper, that the class $mathrm{NU}$ of non-universal separable Banach spaces is strongly bounded. This settles in the affirmative the main conjecture form cite{AD}. Our approach is based, among others, on a construction of $llll_infty$-spaces, due to J. Bourgain and G. Pisier. As a consequence we show that there exists a family ${Y_xi:xi<omega_1}$ of separable, non-universal, $llll_infty$-spaces which uniformly exhausts all separable Banach spaces. A number of other natural classes of separable Banach spaces are shown to be strongly bounded as well." @default.
• W2103014598 created "2016-06-24" @default.
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• W2103014598 date "2008-05-14" @default.
• W2103014598 modified "2023-09-27" @default.
• W2103014598 title "On classes of Banach spaces admitting small universal spaces" @default.
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