Operator-Valued Norms

Abstract

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 $\text{B}$, we provide an $L(C(K))$-valued norm on $\text{B}$. and we introduce an $L(C(K))$-valued norm on a Banach space satisfying special properties.

8 pages

Cited by in corpus (1)

• Banach Spaces with respect to Operator-Valued Norms