论文标题
C* Norm的Gateaux衍生物
Gateaux derivative of C* norm
论文作者
论文摘要
我们找到了$ c^*$ - 代数规范的Gateaux衍生物的表达式。这为我们提供了有关空格的副标题集，平滑点和Birkhoff-James正交性$ \ MATHSCR B（\ MATHCAL H）$和$ C_B（ω）$紧密相关的概念的各种已知结果的替代证明或概括。我们还获得了$ a \ in \ mathscr b（\ mathcal h）$ $ a \ in Norm函数的细分组的表达式，以及操作员$ a \ in \ Mathscr b（\ Mathcal H，\ Mathcal H，\ Mathcal k）$的正交性的表征$ dist（a，\ mathscr k（\ mathcal h，\ mathcal k））<\ | a \ | $。
We find an expression for Gateaux derivative of the $C^*$-algebra norm. This gives us alternative proofs or generalizations of various known results on the closely related notions of subdifferential sets, smooth points and Birkhoff-James orthogonality for spaces $\mathscr B(\mathcal H)$ and $C_b(Ω)$. We also obtain an expression for subdifferential sets of the norm function at $A\in\mathscr B(\mathcal H)$ and a characterization of orthogonality of an operator $A\in\mathscr B(\mathcal H, \mathcal K)$ to a subspace, under the condition $dist(A, \mathscr K(\mathcal H))< \|A\|$ and $dist(A, \mathscr K(\mathcal H, \mathcal K))< \|A\|$ respectively.
