Extending into isometries of <IMG BORDER="0" SRC="/proc/2006-134-07/S0002-9939-06-08178-0/gif-title0/img1.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Extending into isometries of

Authors:	T S S R K Rao

Institution:	Stat--Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Abstract:	In this paper we generalize a result of Hopenwasser and Plastiras (1997) that gives a geometric condition under which into isometries from ${\mathcal K}(\ell^2)$ to ${\mathcal L}(\ell^2)$ have a unique extension to an isometry in ${\mathcal L}({\mathcal L}(\ell^2))$ . We show that when and are separable reflexive Banach spaces having the metric approximation property with strictly convex and smooth and such that ${\mathcal K}(X,Y)$ is a Hahn-Banach smooth subspace of ${\mathcal L}(X,Y)$ , any nice into isometry $\Psi_0 :{\mathcal K}(X,Y)\rightarrow {\mathcal L}(X,Y)$ has a unique extension to an isometry in ${\mathcal L}({\mathcal L}(X,Y))$ .

Keywords:	Isometries Hahn-Banach smooth spaces

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