Research Article

On the Unconditionally $p-$Approximation Property via Lipschitz Operators

Volume: 12 Number: 2 June 30, 2026

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

Ethical Statement

No approval from the Board of Ethics is required.

References

  1. [1] A. Grothendieck, Produits tensoriels topologiques et espaces nucl´eaires, 4th Printing, Memoirs of The American Mathematical Society (16), Rhode Island, 1955.
  2. [2] P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Mathematica 130 (1) (1973) 309–317.
  3. [3] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I and II: Sequence Spaces and Function Spaces, 1st Edition, Springer, 1996.
  4. [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. [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. [6] D. P. Sinha, A. K. Karn, Compact operators whose adjoints factor through subspaces of ℓp, Studia Mathematica 150 (1) (2002) 17–33.
  7. [7] M. Jung, J. M. Kim, Approximation properties in terms of Lipschitz maps, Studia Mathematica 268 (2023) 345–359.
  8. [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

Publication Date

June 30, 2026

Submission Date

March 31, 2026

Acceptance Date

May 21, 2026

Published in Issue

Year 2026 Volume: 12 Number: 2

APA
Keten Çopur, A. (2026). On the Unconditionally $p-$Approximation Property via Lipschitz Operators. Journal of Advanced Research in Natural and Applied Sciences, 12(2), 146-156. https://doi.org/10.28979/jarnas.1919582
AMA
1.Keten Çopur A. On the Unconditionally $p-$Approximation Property via Lipschitz Operators. JARNAS. 2026;12(2):146-156. doi:10.28979/jarnas.1919582
Chicago
Keten Çopur, Ayşegül. 2026. “On the Unconditionally $p-$Approximation Property via Lipschitz Operators”. Journal of Advanced Research in Natural and Applied Sciences 12 (2): 146-56. https://doi.org/10.28979/jarnas.1919582.
EndNote
Keten Çopur A (June 1, 2026) On the Unconditionally $p-$Approximation Property via Lipschitz Operators. Journal of Advanced Research in Natural and Applied Sciences 12 2 146–156.
IEEE
[1]A. Keten Çopur, “On the Unconditionally $p-$Approximation Property via Lipschitz Operators”, JARNAS, vol. 12, no. 2, pp. 146–156, June 2026, doi: 10.28979/jarnas.1919582.
ISNAD
Keten Çopur, Ayşegül. “On the Unconditionally $p-$Approximation Property via Lipschitz Operators”. Journal of Advanced Research in Natural and Applied Sciences 12/2 (June 1, 2026): 146-156. https://doi.org/10.28979/jarnas.1919582.
JAMA
1.Keten Çopur A. On the Unconditionally $p-$Approximation Property via Lipschitz Operators. JARNAS. 2026;12:146–156.
MLA
Keten Çopur, Ayşegül. “On the Unconditionally $p-$Approximation Property via Lipschitz Operators”. Journal of Advanced Research in Natural and Applied Sciences, vol. 12, no. 2, June 2026, pp. 146-5, doi:10.28979/jarnas.1919582.
Vancouver
1.Ayşegül Keten Çopur. On the Unconditionally $p-$Approximation Property via Lipschitz Operators. JARNAS. 2026 Jun. 1;12(2):146-5. doi:10.28979/jarnas.1919582

 

 

 

TR Dizin 20466
 

 

SAO/NASA Astrophysics Data System (ADS)    34270

                                                   American Chemical Society-Chemical Abstracts Service CAS    34922 

 

DOAJ 32869

EBSCO 32870

Scilit 30371                        

SOBİAD 20460

 

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