By A. Aizpuru-Tomas, F. Leon-Saavedra
This quantity contains a suite of articles from specialists with a wealthy learn and academic event. The members of this quantity are: Y Benyamini, M Gonzбlez, V Mьller, S Reich, E Matouskova, A J Zaslavski and A R Palacios. each one in their paintings is necessary. for instance, Benyamini's is the single up to date survey of the interesting and lively sector of the class of Banach areas below uniformly non-stop maps whereas Gonzбlez's article is a pioneer creation to the speculation of neighborhood duality for Banach areas.
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Extra resources for Advanced Courses of Mathematical Analysis I: Proceedings of the First International School
142 (2001), 155-168. 12. M. Gonzalez and A. Martinez-Abej6n. Local dual spaces of Banach spaces of vector-valued functions, Proc. Amer. Math. 130 (2002), 3255-3258. 13. M. Gonzalez and A. Martinez-Abej6n. Ultrapowers and subspaces of the dual of a Banach space, Glasgow Math. , to appear. 14. P. Harmand, D. Werner and W. Werner. M-ideals in Banach spaces and Banach algebras. Lecture Notes in Math. Springer-Verlag, Berlin, 1993. 15. S. Heinrich. Ultraproducts in Banach space theory, J. Reine Angew.
Assume that f : L1 -+ I1 is a surjective uniform homeomorphism. Then f-’ satisfies a Lipschitz condition for large distances and we choose a constant K so that JIy- zll 2 1 implies K - l I l y - 41 I Ilf(y) - f(z)ll. Fix 6 > 0. 1 the set Mid(%,-x, 0) is a “large” subset of L1 for every x E L1: it contains an infinite IIxlI-separated set. 2. After translating the points to x and -x and assuming, as we may, that llxll 2 1, we obtain for this x that this large set is supposed to be mapped by f into Mid(f(z),f(-z),G), which is a “small” set in 11: it is a finite-dimensional perturbation of a set of small diameter.
14. P. Harmand, D. Werner and W. Werner. M-ideals in Banach spaces and Banach algebras. Lecture Notes in Math. Springer-Verlag, Berlin, 1993. 15. S. Heinrich. Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72-104. 16. J. Johnson. Remarks o n Banach spaces of compact operators, J. Funct. Anal. 32 (1979), 304-311. dir 17. B. P. Rosenthal and M. Zippin. O n bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506. 18.
Advanced Courses of Mathematical Analysis I: Proceedings of the First International School by A. Aizpuru-Tomas, F. Leon-Saavedra