Exact and Approximate Operator Parallelism

[摘要] Extending the notion of parallelism we introduce the concept ofapproximate parallelism in normed spaces and then substantiallyrestrict ourselves to the setting of Hilbert space operators endowedwith the operator norm. We present several characterizations of theexact and approximate operator parallelism in the algebra$mathbb{B}(mathscr{H})$ of bounded linear operators acting on aHilbert space $mathscr{H}$. Among other things, we investigate therelationship between approximate parallelism and norm of innerderivations on $mathbb{B}(mathscr{H})$. We also characterize theparallel elements of a $C^*$-algebra by using states. Finally weutilize the linking algebra to give some equivalence assertionsregarding parallel elements in a Hilbert $C^*$-module.

[学科分类] 数学（综合）

[关键词] $C^*$-algebra;approximate parallelism;operator parallelism;Hilbert $C^*$-module