On properties of disjoint sequences in Tzafriri type spaces
https://doi.org/10.26907/2949-3919.2026.1.16-46
Abstract
We study the properties of disjoint sequences in the Tzafriri space T(p, γ) and its modification, the Tirilman space Ti(p, γ). In paticular, it is shown that the space T(p, γ) can be obtained by symmetrization of the canonical unit basis in Ti(p, γ). The lower optimal space, recently introduced by the author in a joint paper with P. Nilsson, is identified for both spaces.
Keywords
Banach lattice,
symmetric space,
upper/lower estimate,
Lorentz space,
Tzafriri space,
Tirilman space
Supporting agencies: This research was supported by the Program of Development of the Regional Scientific and Educational mathematical Center of the Volga Federal District, agreement no. 075-02-2026-1335
About the Author
S. V. Astashkin
Samara National Research University; Moscow State University, Moscow Center for Fundamental and Applied Mathematics; BAU Bahcesehir University
Russian Federation
Russian Federation
Sergey Vladimirovich Astashkin
34 Moskovskoye Hwy, Samara 443086; 1 Leninskie Gory, Moscow, 119991; Istanbul
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For citations:
Astashkin S.V. On properties of disjoint sequences in Tzafriri type spaces. Mathematics and Theoretical Computer Science. 2026;4(1):16-46. (In Russ.) https://doi.org/10.26907/2949-3919.2026.1.16-46
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