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Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space
N. L. Randrianarivony
A map f between two metric spaces (X,d_1) and (Y,d_2) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi_1, phi_2:[0,\infty) --> [0,\infty) suc…
The Diameter of the Isomorphism Class of a Banach Space
W. B. Johnson, E. Odell
We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proo…
An example of an asymptotically Hilbertian space which fails the approximation property
P. G. Casazza, C. L. Garcia, W. B. Johnson
Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the appro…
Geometry of Banach spaces and biorthogonal systems
S. J. Dilworth, Maria Girardi, W. B. Johnson
A separable Banach space X contains isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur…
Nonlinear quotients
Sean M. Bates, William B. Johnson, Joram Lindenstrauss +2
New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are…