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pro vyhledávání: '"Causey, R."'
Autor:
Causey, R. M., Pelczar-Barwacz, A.
We prove that any normalized block sequence in a Schreier space $X_\xi$, of arbitrary order $\xi<\omega_1$, admits a subsequence equivalent to a subsequence of the canonical basis of some Schreier space. The analogous result is proved for dual spaces
Externí odkaz:
http://arxiv.org/abs/2311.00761
Autor:
Causey, R. M.
We provide a short calculation of the Szlenk index of $C(K)$ spaces using the Grasberg norm.
Externí odkaz:
http://arxiv.org/abs/2305.08147
We prove that for infinite, countable, compact, Hausdorff spaces $K,L$, $C(K)\widehat{\otimes}_\pi C(L)$ is isomorphic to exactly one of the spaces $C(\omega^{\omega^\xi})\widehat{\otimes}_\pi C(\omega^{\omega^\zeta})$, $0\leqslant \zeta\leqslant \xi
Externí odkaz:
http://arxiv.org/abs/2201.08271
We study four asymptotic smoothness properties of Banach spaces, denoted $\textsf{T}_p,\textsf{A}_p, \textsf{N}_p$ and $\textsf{P}_p$. We complete their description by proving the missing renorming theorem for $\textsf{A}_p$. We prove that asymptotic
Externí odkaz:
http://arxiv.org/abs/2110.06710
Autor:
Causey, R. M.
Galego and Samuel showed that if $K,L$ are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is $c_0$-saturated if and only if it is subprojective if and only if $K$ and $L$ are both scattered. We remove the hypothesis of m
Externí odkaz:
http://arxiv.org/abs/2012.13440
In this paper we prove that the $3$-fold injective tensor product $\ell_1 \widehat{\otimes}_\varepsilon \ell_1 \widehat{\otimes}_\varepsilon \ell_1 $ is not isomorphic to any subspace of $\ell_1 \widehat{\otimes}_\varepsilon \ell_1$. This result prov
Externí odkaz:
http://arxiv.org/abs/2012.13438
We compute the Szlenk index of an arbitrary projective tensor product $C(K)\widehat{\otimes}_\pi C(L)$ of spaces $C(K), C(L)$ of continuous functions on scattered, compact, Hausdorff spaces. In particular, we show that it is simply equal to the maxim
Externí odkaz:
http://arxiv.org/abs/2012.13439
Autor:
Causey, R. M., Dilworth, Stephen J.
Let $m,n$ be positive integers with $m
Externí odkaz:
http://arxiv.org/abs/2012.13437
Autor:
Causey, R. M.
We use the repeated averages hierarchy to prove a Ramsey theorem regarding uniform upper estimates of convex block sequences of weakly null sequences. The base case of the theorem recovers a result of Freeman.
Externí odkaz:
http://arxiv.org/abs/2003.11166
In the present paper we prove that the $3$-fold projective tensor product of $c_0$, $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$, is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_\pi c_{0}$. In particular, this settles th
Externí odkaz:
http://arxiv.org/abs/2003.09878