Envelope functions and asymptotic structures in Banach spaces

• Autorzy: Bünyamin Sarı
• Języki publikacji: EN

Abstrakty

EN

We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic-$ℓ_{p}$ spaces in terms of the $ℓ_{p}$-behavior of "disjoint-permissible" vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey-Pisier theorem.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B45: Banach sequence spaces
• 46B07: Local theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 164
• Numer: 3
• Strony: 283-306

Daty

wydano

2004

Twórcy

autor

Bünyamin Sarı

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1 Canada

Identyfikatory

DOI

10.4064/sm164-3-6