Asymptotically hilbertian modular Banach spaces : examples of uncountable categoricity

• Autorzy: Henson C. W. , Raynaud Y.

Identyfikatory

DOI

10.14708/cm.v56i1.1231

• Języki publikacji: EN

Abstrakty

EN

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⊕_mH, where H is an arbitrary Hilbert space and ⊕_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.

Słowa kluczowe

EN

Banach spaces; ultrapowers; elementary equivalence; isometric embeddings; modular direct sums

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 1
• Strony: 119--144
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Henson C. W.

• University of Illinois at Urbana Champaign (UIUC), Urbana, Illinois 61801, United States

autor

Raynaud Y.

• Institut de Mathématiques de Jussieu-Paris Rive Gauche CNRS/UPMC (University Paris-06) Univ.Paris-Diderot, 4 place Jussieu, F-75252 Paris Cedex 05, France

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.