Linear and Multilinear Algebra ( IF 1.1 ) Pub Date : 2023-04-15 , DOI: 10.1080/03081087.2023.2198758 Divya Khurana
We present a complete characterization of the right-symmetric points in the one sum of two Banach spaces. We also obtain some basic properties of the left-symmetric (right-symmetric) points in the p sum, (), of two Banach spaces. Using these properties we (a) give examples of Banach spaces which do not have any non-zero left-symmetric points and (b) prove a complete characterization of those left-symmetric and right-symmetric points in the p sum, , of two Banach spaces, whose components satisfy an additional norm assumption. We give examples of Banach spaces where all non-zero left-symmetric or right-symmetric points satisfy this additional norm assumption. We also present an alternative proof of the recently obtained characterization of the left-symmetric and the right-symmetric points in , , and , .
中文翻译:
Banach 空间中 Birkhoff-James 正交性的局部对称性研究
我们呈现了两个 Banach 空间的和中右对称点的完整特征。我们还得到了p和中左对称(右对称)点的一些基本性质,(), 两个 Banach 空间。使用这些属性,我们 ( a ) 给出了没有任何非零左对称点的 Banach 空间的示例,并且 ( b ) 证明了p和中那些左对称和右对称点的完整表征,,两个 Banach 空间的,其组件满足附加范数假设。我们给出 Banach 空间的示例,其中所有非零左对称或右对称点都满足此附加范数假设。我们还提供了最近获得的左对称点和右对称点特征的替代证明,, 和,.