Weak Approximation Properties Induced by Unconditionally p-Compact Sets
- 1Department of Mathematics and Computer Science, Faculty of Sciences, Necmettin Erbakan University, Konya 42090, Türkiye
Abstract
This paper investigates several equivalent formulations of the unconditionally p-approximation property. Inspired by these formulations, we introduce a new approximation property, called the weak unconditionally p-approximation property, and develop a number of equivalent characterizations for it. We also examine its relationship with the corresponding duality problem and obtain a partial answer. In addition, the weak bounded approximation property is reinterpreted within the framework of unconditionally p-compact sets, leading to new characterizations. Finally, we establish a three-space result for the weak unconditionally p-approximation property by showing that this property is preserved under suitable assumptions on a complemented subspace and the corresponding quotient space.
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BibTeX
@article{copur2026weak,
title = {{Weak Approximation Properties Induced by Unconditionally p-Compact Sets}},
author = {Ayşegül Keten Çopur},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203776},
url = {https://www.mdpi.com/2227-7390/14/20/3776},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Weak Approximation Properties Induced by Unconditionally p-Compact Sets
AU - Ayşegül Keten Çopur
PY - 2026
DA - 2026/10/18
JO - Mathematics
DO - 10.3390/math14203776
UR - https://www.mdpi.com/2227-7390/14/20/3776
AB - This paper investigates several equivalent formulations of the unconditionally p-approximation property. Inspired by these formulations, we introduce a new approximation property, called the weak unconditionally p-approximation property, and develop a number of equivalent characterizations for it. We also examine its relationship with the corresponding duality problem and obtain a partial answer. In addition, the weak bounded approximation property is reinterpreted within the framework of unconditionally p-compact sets, leading to new characterizations. Finally, we establish a three-space result for the weak unconditionally p-approximation property by showing that this property is preserved under suitable assumptions on a complemented subspace and the corresponding quotient space.
SN - 2227-7390
ER -