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, $1\le p\ne 2<\mathrm{\infty }$ ($1<p\ne 2<\mathrm{\infty }$), 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, $1<p\ne 2<\mathrm{\infty }$, 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 ${\ell }_p^n$, $n\ge 3$, and ${\ell }_p$, $1\le p\ne 2<\mathrm{\infty }$.

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，$\mathrm{1个}\le p\ne \mathrm{2个}<\mathrm{\infty }$($\mathrm{1个}<p\ne \mathrm{2个}<\mathrm{\infty }$), 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，$\mathrm{1个}<p\ne \mathrm{2个}<\mathrm{\infty }$，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${\ell }_p^n$,$n\ge \mathrm{3个}$， 和${\ell }_p$,$\mathrm{1个}\le p\ne \mathrm{2个}<\mathrm{\infty }$.