Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

C. Ward Henson, and Yves Raynaud. "Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity." Commentationes Mathematicae 56.1 (2016): null. <http://eudml.org/doc/292422>.

@article{C2016,
abstract = {We give a criterion ensuring that the elementary class of a modular Banach space $E$ (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of $E$) consists of all direct sums $E\oplus _m H$, where $H$ is an arbitrary Hilbert space and $\oplus _m$ denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.},
author = {C. Ward Henson, Yves Raynaud},
journal = {Commentationes Mathematicae},
keywords = {Banach spaces; ultrapowers; elementary equivalence; isometric embeddings; modular direct sums},
language = {eng},
number = {1},
pages = {null},
title = {Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity},
url = {http://eudml.org/doc/292422},
volume = {56},
year = {2016},
}

TY - JOUR
AU - C. Ward Henson
AU - Yves Raynaud
TI - Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity
JO - Commentationes Mathematicae
PY - 2016
VL - 56
IS - 1
SP - null
AB - We give a criterion ensuring that the elementary class of a modular Banach space $E$ (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of $E$) consists of all direct sums $E\oplus _m H$, where $H$ is an arbitrary Hilbert space and $\oplus _m$ denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures.
LA - eng
KW - Banach spaces; ultrapowers; elementary equivalence; isometric embeddings; modular direct sums
UR - http://eudml.org/doc/292422
ER -