Extending into isometries of $\mathcal {K}(X,Y)$
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- by T. S. S. R. K. Rao PDF
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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 $X$ and $Y$ are separable reflexive Banach spaces having the metric approximation property with $X$ strictly convex and $Y$ 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 ${\mathcal L}({\mathcal L}(X,Y))$.References
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Additional Information
- T. S. S. R. K. Rao
- Affiliation: Stat–Math Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India
- MR Author ID: 225502
- ORCID: 0000-0003-0599-9426
- Email: tss@isibang.ac.in
- Received by editor(s): November 8, 2004
- Received by editor(s) in revised form: February 15, 2005
- Published electronically: January 5, 2006
- Additional Notes: This work was done under DST-NSF project DST/INT/US(NSF-RPO-0141)/2003
- Communicated by: Joseph A. Ball
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 2079-2082
- MSC (2000): Primary 47L05, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-06-08178-0
- MathSciNet review: 2215777