论文标题
双线性操作员的标准衍生物和几何形状
Norm derivatives and geometry of bilinear operators
论文作者
论文摘要
我们在实际Banach空间中的Birkhoff-James正交性的背景下研究规范导数。作为此的应用，我们可以从范数衍生物中获得左对称点和右对称点的完整表征。我们获得了$ \ ell_1^n $和$ \ ell_ \ infty^n $空间中强的Birkhoff-James正交性的完整表征。我们还获得了由标准衍生物定义的正交关系的完整表征，该关系是根据Birkhoff-James正交性的一些新引入的变化而定义的。我们进一步研究Birkhoff-James的正交性，近似Birkhoff-James的正交性，平滑度和在Banach空间之间有界双线运算符的规范。
We study the norm derivatives in the context of Birkhoff-James orthogonality in real Banach spaces. As an application of this, we obtain a complete characterization of the left-symmetric points and the right-symmetric points in a real Banach space in terms of the norm derivatives. We obtain a complete characterization of strong Birkhoff-James orthogonality in $\ell_1^n$ and $\ell_\infty^n$ spaces. We also obtain a complete characterization of the orthogonality relation defined by the norm derivatives in terms of some newly introduced variation of Birkhoff-James orthogonality. We further study Birkhoff-James orthogonality, approximate Birkhoff-James orthogonality, smoothness and norm attainment of bounded bilinear operators between Banach spaces.
