Rank $\alpha $ operators on the space $C(T,X)$
Volume 91 / 2002
Colloquium Mathematicum 91 (2002), 255-262
MSC: 46A32, 46B28, 46E15, 46M05, 47A80, 47B10, 47B38.
DOI: 10.4064/cm91-2-5
Abstract
For $0\leq \alpha <1$, an operator $U\in L(X,Y)$ is called a rank $\alpha $ operator if $x_{n}\mathrel {\mathop { \rightarrow }\limits ^{\tau _{\alpha }}}x$ implies $Ux_{n}\rightarrow Ux$ in norm. We give some results on rank $\alpha $ operators, including an interpolation result and a characterization of rank $\alpha $ operators ${U:C(T,X)\rightarrow Y}$ in terms of their representing measures.
