Operator-Valued Norms
Abstract
Description
We introduce two kinds of operator-valued norms. One of them is an $L(H)$-valued norm. The other one is an $L(C(K))$-valued norm. We characterize the completeness with respect to a bounded $L(H)$-valued norm. Furthermore, for a given Banach space $\textbf{B}$, we provide an $L(C(K))$-valued norm on $\textbf{B}$. and we introduce an $L(C(K))$-valued norm on a Banach space satisfying special properties.
8 pages
8 pages