arXiv subjects
Publications and source records attributed to Anna Maria Pelczar.
We prove quasiminimality of the regular mixed Tsirelson spaces T[(S_n,θ_n)_n] with the sequence (\frac{θ_n}{θ^n})_n decreasing, where θ=\lim_n θ_n^{1/n}, and quasiminimality of all mixed Tsirelson spaces T[(A_n,θ_n)_n]. We prove that under certain assumptions on the sequence (θ_n)_n the dual spaces are quasiminimal.
The relation between different notions measuring proximity to $\ell_1$ and distortability of a Banach space is studied. The main result states that a Banach space, whose all subspaces have Bourgain $\ell_1$ index greater than $ω^α$, $α<ω_1$, contains either an arbitrary distortable subspace or an $\ell_1^α$-asymptotic subspace.
We consider classical Tsirelson-type norms of $T[A_r,θ]$ and their modified versions on $\ell_p$ spaces. We show that for any $1<p<\infty$ there is a constant $λ_p$ such that considered Tsirelson-type norms do not $λ_p$-distort any of subspaces of $\ell_p$.
We consider a normalized basis in a Banach space with the following property: any normalized block sequence of the basis has a subsequence equivalent to the basis. We show that under uniformity or other natural assumptions, a basis with this property is equivalent to the unit vector basis of $c_0$ or $\ell_p$. We also address an analogous problem for spreading models.
We show that every Banach space saturated with subsymmetric sequences contains a minimal subspace.