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ℓ¹-Spreading models in subspaces of mixed Tsirelson spaces

Denny H. Leung, Wee-Kee Tang (2006)

Studia Mathematica

We investigate the existence of higher order ℓ¹-spreading models in subspaces of mixed Tsirelson spaces. For instance, we show that the following conditions are equivalent for the mixed Tsirelson space X = T [ ( θ ₙ , ₙ ) n = 1 ∞ ] : (1) Every block subspace of X contains an ℓ ¹ - ω -spreading model, (2) The Bourgain ℓ¹-index I b ( Y ) = I ( Y ) > ω ω for any block subspace Y of X, (3) l i m ₘ l i m s u p ₙ θ m + n / θ ₙ > 0 and every block subspace Y of X contains a block sequence equivalent to a subsequence of the unit vector basis of X. Moreover, if one (and hence all) of these conditions...

Lacunary weak statistical convergence

Fatih Nuray (2011)

Mathematica Bohemica

The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and ℐ -convergence to weak ℐ -convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequence. We find a connection between weak lacunary statistical convergence and weak statistical convergence.

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