تقرير
A class of summing operators acting in spaces of operators
العنوان: | A class of summing operators acting in spaces of operators |
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المؤلفون: | Rodríguez, J., Sánchez-Pérez, E. A. |
سنة النشر: | 2020 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Functional Analysis, 46G10, 47B10 |
الوصف: | Let $X$, $Y$ and $Z$ be Banach spaces and let $U$ be a subspace of $\mathcal{L}(X^*,Y)$, the Banach space of all operators from $X^*$ to $Y$. An operator $S: U \to Z$ is said to be $(\ell^s_p,\ell_p)$-summing (where $1\leq p <\infty$) if there is a constant $K\geq 0$ such that $$ \Big( \sum_{i=1}^n \|S(T_i)\|_Z^p \Big)^{1/p} \le K \sup_{x^* \in B_{X^*}} \Big(\sum_{i=1}^n \|T_i(x^*)\|_Y^p\Big)^{1/p} $$ for every $n\in \mathbb{N}$ and every $T_1,\dots,T_n \in U$. In this paper we study this class of operators, introduced by Blasco and Signes as a natural generalization of the $(p,Y)$-summing operators of Kislyakov. On one hand, we discuss Pietsch-type domination results for $(\ell^s_p,\ell_p)$-summing operators. In this direction, we provide a negative answer to a question raised by Blasco and Signes, and we also give new insight on a result by Botelho and Santos. On the other hand, we extend to this setting the classical theorem of Kwapie\'{n} characterizing those operators which factor as $S_1\circ S_2$, where $S_2$ is absolutely $p$-summing and $S_1^*$ is absolutely $q$-summing ($1
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نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2003.07252 |
رقم الأكسشن: | edsarx.2003.07252 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |