Numerical Radius Norms on Operator Spaces

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dc.creatorItoh, Takashi
dc.creatorNagisa, Masaru
dc.date2004-04-07
dc.date.accessioned2026-07-07T05:07:15Z
dc.date.available2026-07-07T05:07:15Z
dc.descriptionWe introduce a numerical radius operator space $(X, \mathcal{W}_n)$. The conditions to be a numerical radius operator space are weaker than the Ruan's axiom for an operator space $(X, \mathcal{O}_n)$. Let $w(\cdot)$ be the numerical radius norm on $\mathbb{B}(\mathcal{H})$. It is shown that if $X$ admits a norm $\mathcal{W}_n(\cdot)$ on the matrix space $\mathbb{M}_n(X)$ which satisfies the conditions, then there is a complete isometry, in the sense of the norms $\mathcal{W}_n(\cdot)$ and $w_n(\cdot)$, from $(X, \mathcal{W}_n)$ into $(\mathbb{B}(\mathcal{H}), w_n)$. We study the relationship between the operator space $(X, \mathcal{O}_n)$ and the numerical radius operator space $(X, \mathcal{W}_n)$. The category of operator spaces can be regarded as a subcategory of numerical radius operator spaces.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/math/0404153
dc.identifierhttp://arxiv.org/abs/math/0404153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70785
dc.subjectOperator Algebras
dc.subject46L07 (Primary) 46L06, 47L25 (Secondary)
dc.titleNumerical Radius Norms on Operator Spaces
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