On the Unconditionally $p-$Approximation Property via Lipschitz Operators
Abstract
This paper studies an extension of the unconditionally $p-$approximation property to the framework of Lipschitz operator theory. Motivated by the notion of the unconditionally $p-$approximation property defined via unconditionally $p-$compact sets, we introduce the Lipschitz unconditionally $p-$approximation property and establish several characterizations of this new property. Moreover, we obtain new characterizations of the unconditionally $p-$approximation property in terms of Lipschitz operators.
Keywords
- Approximation property
- unconditionally $p-$approximation property
- Lipschitz operators
- Lipschitz-free spaces
- unconditionally $p-$compact sets
Ethical Statement
References
- [1] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, 4th Printing, Memoirs of The American Mathematical Society (16), Rhode Island, 1955.
- [2] P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Mathematica 130 (1) (1973) 309–317.
- [3] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I and II: Sequence Spaces and Function Spaces, 1st Edition, Springer, 1996.
- [4] P. G. Casazza, Approximation properties, in: W. B. Johnson, J. Lindenstrauss (Eds.), Vol. 1 of Handbook of the Geometry of Banach Spaces, Elsevier, Amsterdam, 2001, pp. 271–316.
- [5] C. Choi, J. M. Kim, Weak and quasi approximation properties in Banach spaces, Journal of Mathematical Analysis and Applications 316 (2) (2006) 722–735.
- [6] D. P. Sinha, A. K. Karn, Compact operators whose adjoints factor through subspaces of ℓp, Studia Mathematica 150 (1) (2002) 17–33.
- [7] M. Jung, J. M. Kim, Approximation properties in terms of Lipschitz maps, Studia Mathematica 268 (2023) 345–359.
- [8] A. Mandal, Approximation property in terms of Lipschitz maps via tensor product approach, (2025) Accessed 10 Jan 2026.
Details
Primary Language
English
Subjects
Operator Algebras and Functional Analysis
Journal Section
Research Article
Authors
Publication Date
June 30, 2026
Submission Date
March 31, 2026
Acceptance Date
May 21, 2026
Published in Issue
Year 2026 Volume: 12 Number: 2