Abstract
We introduce a concept of antisymmetric Arens regularity of Banach spaces and prove that a Banach space is Arens regular if and only if it is both symmetrically Arens regular and antisymmetrically Arens regular.
We show that if a Banach space is nonreflexive, then it is not antisymmetrically Arens regular and provide an example of a symmetrically Arens regular Banach space which is not antisymmetrically Arens regular.
Key words: Banach space, Arens regularity, James type space.
Full Text
Article Information
| Title | Antisymmetric Arens Regularity |
| Source | Methods Funct. Anal. Topology, Vol. 32 (2026), no. 2, 193-199 |
| DOI | 10.31392/MFAT-npu26_2.2026.09 |
| Milestones | Received 04/05/2026; Revised 31/05/2026 |
| Copyright | The Author(s) 2026 (CC BY-SA) |
Authors Information
Taras Vasylyshyn
Department of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
Yurii Sharyn
Department of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
Citation Example
Taras Vasylyshyn and Yurii Sharyn, Antisymmetric Arens Regularity, Methods Funct. Anal. Topology 32
(2026), no. 2, 193-199.
BibTex
@article {MFAT2284,
AUTHOR = {Taras Vasylyshyn and Yurii Sharyn},
TITLE = {Antisymmetric Arens Regularity},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {32},
YEAR = {2026},
NUMBER = {2},
PAGES = {193-199},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_2.2026.09},
URL = {https://mfat.imath.kiev.ua/article/?id=2284},
}
