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pro vyhledávání: '"Causey, Ryan M"'
Autor:
Causey, Ryan M.
For each ordinal $\xi$ and each $1\leqslant q<\infty$, we define the notion of $\xi$-$q$-summable Szlenk index. When $\xi=0$ and $q=1$, this recovers the usual notion of summable Szlenk index. We define for an arbitrary weak$^*$-compact set a transfi
Externí odkaz:
http://arxiv.org/abs/1801.00033
We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for example, to the `automatic-type' phenomenon, the type-cotype duality, o
Externí odkaz:
http://arxiv.org/abs/1712.04208
Autor:
Beanland, Kevin, Causey, Ryan M.
A bounded linear operator $U$ between Banach spaces is universal for the complement of some operator ideal $\mathfrak{J}$ if it is a member of the complement and it factors through every element of the complement of $\mathfrak{J}$. In the first part
Externí odkaz:
http://arxiv.org/abs/1711.09244
Autor:
Causey, Ryan M., Lancien, Gilles
In a previous work, the first named author described the set $\cal P$ of all values of the Szlenk indices of separable Banach spaces. We complete this result by showing that for any integer $n$ and any ordinal $\alpha$ in $\cal P$, there exists a sep
Externí odkaz:
http://arxiv.org/abs/1710.01638
Autor:
Causey, Ryan M
We provide a short characterization of $p$-asymptotic uniform smoothability and asymptotic uniform flatenability of operators and of Banach spaces. We use these characterizations to show that many asymptotic uniform smoothness properties pass to inje
Externí odkaz:
http://arxiv.org/abs/1705.05484
Autor:
Causey, Ryan M.
Given a Banach space $X$, a $w^*$-compact subset of $X^*$, and $1
Externí odkaz:
http://arxiv.org/abs/1701.06226
Autor:
Causey, Ryan M
We prove the optimal estimate between the Szlenk and $w^*$-dentability indices of an arbitrary $w^*$-compact subset of the dual of a Banach space. For a given $w^*$-compact, convex subset $K$ of the dual of a Banach space, we introduce a two player g
Externí odkaz:
http://arxiv.org/abs/1608.03668
Autor:
Causey, Ryan M
We extend a precise renorming result of Godefroy, Kalton, and Lancien regarding asymptotically uniformly smooth norms of separable Banach spaces with Szlenk index $\omega$. For every ordinal $\xi$, we characterize the operators, and therefore the Ban
Externí odkaz:
http://arxiv.org/abs/1608.03666