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Envelope functions and asymptotic structures in Banach spaces

100%

Sarı B.

Studia Mathematica

2004

tom 164

nr 3

283-306

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.

On the structure of the set of higher order spreading models

63%

Sarı B., Tyros K.

Studia Mathematica

2014

tom 223

nr 2

149-173

We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set $SM_{ξ}^{w}(X)$ of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if $SM_{ξ}^{w}(X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $SM_{ξ}^{w}(X)$ is uncountable, then it contains an antichain of size continuum.

Ograniczanie wyników

2 Studia Mathematica

2 Sarı B.

1 Tyros K.

1 2014

1 2004

Wyniki wyszukiwania

Envelope functions and asymptotic structures in Banach spaces

On the structure of the set of higher order spreading models