arXiv subjects

A. Pelczar-Barwacz

Publications and source records attributed to A. Pelczar-Barwacz.

2 recordsLinked to original sources

arXiv2023

Equivalence of block sequences in Schreier spaces and their duals

We prove that any normalized block sequence in a Schreier space $X_ξ$, of arbitrary order $ξ<ω_1$, admits a subsequence equivalent to a subsequence of the canonical basis of some Schreier space. The analogous result is proved for dual spaces to Schreier spaces. Basing on these results, we examine the structure of strictly singular operators on Schreier spaces and show that there are $2^\mathfrak{c}$ many closed operator ideals on a Schreier space of any order, its dual and bidual space.

math.FA↗

arXiv2013

Types of tightness in spaces with unconditional basis

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces, but contrary to the recently constructed space of type (4) also tight with constants, thus essentially extending the list of known examples in Gowers classification program. The space is defined on the base on a boundedly modified mixed Tsirelson space with use of a special coding function.

math.FA↗