波兰科学研究院数学研究所
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作者:Zhenghua Luo , Bentuo Zheng
来源:[J].Studia Mathematica(IF 0.549), 2020, Vol.250, pp.19-34IMPAS
摘要:A normed space $X$ is said to have the ball-covering property (BCP,for short) if its unit sphere can be covered by the union of countablymany closed balls not containing the origin. Let $(\varOmega, \varSigma, \mu)$ bea separable measure space and $X$ be a normed space. We show t...
作者:Dongyang Chen , William B. Johnson , Bentuo Zheng
来源:[J].Studia Mathematica(IF 0.549), 2014, Vol.223, pp.187-191IMPAS
摘要:We give a corrected proof of Theorem 2.10 in our paper “Commutators on $(\sum \ell _q)_p$” [Studia Math. 206 (2011),175–190] for the case $1< q< p< \infty $. The case when $1=q< p< \infty $ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that pape...
作者:Bentuo Zheng
来源:[J].Studia Mathematica(IF 0.549), 2006, Vol.176, pp.177-190IMPAS
摘要:Let $1< p< \infty$. Let $X$ be a subspace of a space $Z$ witha shrinking F.D.D. $(E_n)$ which satisfies a block lower-$p$estimate. Then any bounded linear operator $T$ from $X$ whichsatisfies an upper-$(C,p)$-tree estimate factors through asubspace of $(\sum F_n)_{l_p}$, where $(...
作者:Bentuo Zheng
来源:[J].Studia Mathematica(IF 0.549), 2008, Vol.185, pp.87-98IMPAS
摘要:Let $1< q< p< \infty$ and $q\leq r\leq p$. Let $X$ be a reflexive Banach space satisfying a lower-$\ell_q$-tree estimate and let $T$ be a bounded linear operator from $X$ which satisfies an upper-$\ell_p$-tree estimate. Then $T$ factors through a subspace of $(\sum F_n)_{\ell_r}$...
作者:Dongyang Chen , William B. Johnson , Bentuo Zheng
来源:[J].Studia Mathematica(IF 0.549), 2011, Vol.206, pp.175-190IMPAS
摘要:Let $T$ be a bounded linear operator on $X=(\sum \ell_{q})_{{p}}$ with $1\le q < \infty$and $1< p< \infty$. Then $T$ is a commutator if and only if for all non-zero $\lambda\in \mathbb{C}$, the operator$T-\lambda I$ is not $X$-strictly singular.

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