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A note on biorthogonal systems
Revista Matemática Complutense ( IF 1.4 ) Pub Date : 2020-01-25 , DOI: 10.1007/s13163-019-00339-6
Petr Hájek , Michal Johanis

We consider the following problem (which is a generalisation of a folklore result Proposition 1 below): given a continuous linear operator \(T:X\rightarrow Y\), where Y is a Banach space with a (long) sub-symmetric basis, under which conditions can we find a continuous linear operator \(S:X\rightarrow Y\) such that \(S(B_X)\) contains the basis of Y. As a tool we also consider a non-separable version of Theorem 2 below: Given an infinite subset \(A\subset X^*\), under which conditions can we find a biorthogonal system in \(X\times A\) of cardinality \({{\,\mathrm{card}\,}}A\)?

中文翻译:

关于双正交系统的注释

我们考虑以下问题(以下是民俗结果命题1的推广):给定连续线性算子\(T:X \ rightarrow Y \),其中Y是具有(long)次对称基础的Banach空间,在这种情况下,我们可以找到一个连续的线性算子\(S:X \ rightarrow Y \)使得\(S(B_X)\)包含Y的基。作为工具,我们还考虑以下定理2的不可分版本:给定无限子集\(A \ subset X ^ * \),在这种情况下,我们可以在\(X \ times A \)中找到双正交系统基数\({{\,\ mathrm {card} \,}} A \)吗?
更新日期:2020-01-25
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