Operator-Valued Norms

Details Operator-Valued Norms Operator-Valued Norms

2007-03-08

arxiv.org/abs/math/0703224v2

Mathematics

Functional Analysis

8 pages

Scientific paper

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.

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