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Paths between Banach spaces

Published online by Cambridge University Press:  25 July 2002

M. I. Ostrovskii
M. I. Ostrovskii
Affiliation:
Department of Mathematics, The Catholic University of America, Washington DC, 20064, USA Mathematical Division, Institute for Low Temperature Physics, 47 Lenin Avenue, 61164 Kharkov, Ukraine e-mail: ostrovskii@cua.edu
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Abstract

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The Kadets path distance between Banach spaces X and Y is defined to be the infimum of the lengths with respect to the Kadets distance of all curves joining X and Y. If there is no curve joining X and Y, the Kadets path distance between X and Y is defined to be infty .

Some approaches to estimates of the Kadets path distance from above and from below are developed. In particular, the Kadets path distances between the spaces l_p^n,\ p\in [1,+\rm (inf)ty ], n\in {\b (N)} are estimated.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 2 , May 2002 , pp. 261 - 273
Copyright
2002 Glasgow Mathematical Journal Trust