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Article

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Title

Monotonicities of quasi-normed Calderón–Lozanovskiĭ spaces with applications to approximation problems

Authors

[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[7.4] Mathematics

Year of publication

2024

Published in

Mathematische Nachrichten

Journal year: 2024 | Journal volume: early view/in press

Article type

scientific article

Publication language

english

Keywords
EN
  • best dominated approximation
  • monotonicity properties
  • quasi-normed Calderón–Lozanovskiĭ space
  • quasi-normed ideal space
  • quasi-normed Orlicz spaces
Abstract

EN We consider the geometric structure of quasi-normed Calderón–Lozanovskiĭ spaces. First, we study relations between the quasi-norm and the quasi-modular “near zero” and “near one,” which are fundamental for the theory. With their help, we provide a precise description of the basic monotonicity properties. In comparison with the well-known normed case, we develop a number of new techniques and methods, among which the conditions Δ𝜀 and Δ2−𝑠𝑡𝑟 play a crucial role. From our general results, we conclude the criteria for monotonicity properties in quasi-normed Orlicz spaces, which are new even in this particular context.We consider both the function and the sequence case aswell aswe admit degenerated Orlicz functions, which provides us with a maximal class of spaces under consideration. We also discuss the applications of suitable properties to the best dominated approximation problems in quasi-Banach lattices.

Pages (from - to)

1 - 34

DOI

10.1002/mana.202400013

URL

https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.202400013#:~:text=We%20consider%20the%20geometric%20structure%20of?msockid=043b5dab4bc96af4067e49c14a426bff

Ministry points / journal

100

Impact Factor

0,8 [List 2023]

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