Banach spaces determined by their uniform structures Academic Article

abstract

• Following results of Bourgain and Gorelik we show that the spaces p, 1 < p < , as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0. then it is isomorphic to c0. We show also that there are Banach spaces which are uniformly homeomorphic to exactly 2 isomorphically distinct spaces.

authors

• Johnson, William

published proceedings

• GEOMETRIC AND FUNCTIONAL ANALYSIS

author list (cited authors)

• Johnson, W. B., Lindenstrauss, J., & Schechtman, G.

complete list of authors

• Johnson, WB||Lindenstrauss, J||Schechtman, G

publication date

• December 1996

published in

• GEOMETRIC AND FUNCTIONAL ANALYSIS  Journal

start page

• 430

end page

• 470

volume

• 6

issue

• 3