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Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

100%

Henson C. W., Raynaud Y.

Commentationes Mathematicae

2016

tom 56

nr 1

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.

Some Ramsey type theorems for normed and quasinormed spaces

71%

Henson C. W., Kalton N. J., Tenney Peck N., Tereščák I., Zlatoš P.

Studia Mathematica

1997

tom 124

nr 1

81-100

We prove that every bounded, uniformly separated sequence in a normed space contains a "uniformly independent" subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in $L_p[0,1]$ for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

2 Henson C. W.

1 Kalton N. J.

1 Raynaud Y.

1 Tenney Peck N.

1 Tereščák I.

1 Zlatoš P.

1 2016

1 1997

Wyniki wyszukiwania

Asymptotically hilbertian modular Banach spaces: examples of uncountable categoricity

Some Ramsey type theorems for normed and quasinormed spaces