Operator-Valued Norms

Yun-Su Kim

Operator-Valued Norms

Functional Analysis 2007-05-23 v2 Operator Algebras

Authors: Yun-Su Kim

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 $\textbf{B}$ , 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.

Keywords

banach space operator theory on banach spaces operator theory

Cite

@article{arxiv.math/0703224,
  title  = {Operator-Valued Norms},
  author = {Yun-Su Kim},
  journal= {arXiv preprint arXiv:math/0703224},
  year   = {2007}
}

Comments

8 pages

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