CONTENTSIntroduction..............................................................................................5 I. Basic definitions and notation..............................................................6 M-bases and finite-dimensional decompositions....................................6 Some geometric properties of Banach spaces.......................................9 II. Constructions of equivalent norms.....................................................12 III. (p,q)-estimates in interpolation spaces..............................................21 IV. Geometric properties of operators....................................................26 Nearly uniformly convex operators........................................................27Nearly uniformly smooth operators.........................................................30 V. Factoring operators through nearly uniformly convex spaces...........35 Factorizations and geometric properties of operators..........................35 The case of spaces with finite-dimensional decompositions.................40References.............................................................................................45
1991 Mathematics Subject Classification: 46B03, 46B10, 46B70, 47A05.
@book{bwmeta1.element.zamlynska-27804d1b-c88a-4147-b07e-8252e9f4ac7f,
author = {Prus Stanis\l aw},
title = {Banach spaces and operators which are nearly uniformly convex},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1997},
zbl = {0886.46017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-27804d1b-c88a-4147-b07e-8252e9f4ac7f}
}
Prus Stanisław. Banach spaces and operators which are nearly uniformly convex. GDML_Books (1997), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-27804d1b-c88a-4147-b07e-8252e9f4ac7f/