论文标题
有关特殊有限模块化功能的Hilbert C*模型类别的规律性结果
Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals
论文作者
论文摘要
考虑到J. $ r_0：n \ to $ m $上的$消失。换句话说，零功能从$ m $到$ n $的扩展的独特性是重点的。我们在W*-ergebras上的任何此类Hilbert C*模块上显示了这种延伸的独特性，单调完整的C*-Algebras以及紧凑的C*-Algebras。此外，对于任何C*-Algebra的任何单方面最大模块化理想，延伸的唯一性也会发生。对于给定的一对完整的Hilbert C*-Modules $ M \ subseteq n $，在给定的c*-algebra $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a-linear linear-linear-ableable linearbleable linable octotor $ t_0： W.R.T. $ n $，包含$ m $。这是对可能出现在Hilbert C*模块理论中的有限模块化运算符属性的新观点。顺便说一句，在单调完整和紧凑的C*-ergebras的情况下，我们找到了[13，引理2.4]的正确证明，但在一般C*-case中没有。
Considering the deeper reasons of the appearance of a remarkable counterexample by J.~Kaad and M.~Skeide [17] we consider situations in which two Hilbert C*-modules $M \subset N$ with $M^\bot = \{ 0 \}$ over a fixed C*-algebra $A$ of coefficients cannot be separated by a non-trivial bounded $A$-linear functional $r_0: N \to A$ vanishing on $M$. In other words, the uniqueness of extensions of the zero functional from $M$ to $N$ is focussed. We show this uniqueness of extension for any such pairs of Hilbert C*-modules over W*-algebras, over monotone complete C*-algebras and over compact C*-algebras. Moreover, uniqueness of extension takes place also for any one-sided maximal modular ideal of any C*-algebra. Such a non-zero separating bounded $A$-linear functional $r_0$ exist for a given pair of full Hilbert C*-modules $M \subseteq N$ over a given C*-algebra $A$ iff there exists a bounded $A$-linear non-adjointable operator $T_0: N \to N$ such that the kernel of $T_0$ is not biorthogonally closed w.r.t. $N$ and contains $M$. This is a new perspective on properties of bounded modular operators that might appear in Hilbert C*-module theory. By the way, we find a correct proof of [13, Lemma 2.4] in the case of monotone complete and compact C*-algebras, but not in the general C*-case.
