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Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

On a theorem of Terzioğlu

Asuman Güven AKSOY
Pages
258–267
Publication Date
2022-11-04
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also prove a similar characterization theorem for Q-compact maps.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The theory of compact linear operators acting on a Banach space has a classical core and is familiar tomany.
📊
Key Findings & Data:Perhaps less known is the characterization theorem of Terzioğlu for compact maps.
💡
Conclusion & Impact:We also prove a similar characterization theorem for Q-compact maps.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The theory of compact linear operators acting on a Banach space has a classical core and is familiar tomany. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a numberof important connections that deserves illumination. In this paper we survey Terzioğlu’s characterization theorem forcompact maps and some of its consequences. We also prove a similar characterization theorem for Q-compact maps.

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Cite This Article

AKSOY, A. G. (2022). On a theorem of Terzioğlu. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 258–267. https://ajindex.com/articles/607672

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References (22)

  1. Aksoy AG. Q-Compact sets and Q-compact maps. Math Japon 1991; 36: 1-7
  2. Aksoy, AG, Almira J. On approximation schemes and compactness. In: Proceedings of the First Conference on Classical and Functional Analysis; Azuga, Romania; 2014. pp. 5-24
  3. Aksoy AG, Nakamura M. The approximation numbers n(T) and Q-compactness. Math Japon 1986; 31: 827-840
  4. Astala K. On measures of non-compactness and ideal variations in Banach spaces. Ann Acad Sci Fenn Ser AI Math 1980; 29: 1-42
  5. Brudnyi YuA, Krugljak NYa. On a Family of Approximation Spaces. Studies in the Theory of Function Theory of Several Real Variables, No
  6. Yaroslavl, USSR: Yaroslavl State University, 1978 (in Russian)
  7. Butzer PL, Scherer K. Approximation-Prozesse und Interpolations-Methoden. Mannheim, Germany: Biliographisches Institut, 1968 (in German)
  8. Diestel J. Sequences and Series in Banach Spaces. Berlin, Germany: Springer-Verlag, 1984
  9. Enflo P. A counter example to the approximation property in Banach spaces. Acta Math 1973; 130: 309-317
  10. Fernandez DL, Mastylo M, Da Silva EB. Quasi s-numbers and measures of non-compactness of multilinear operators. Ann Acad Sci-Fi Fenn Math 2013; 38: 805-823
  11. Fourie JH. Injective and surjective hulls of classical p-compact operators with applications to unconditionally pcompact operators. Studia Math 2018; 240: 147-159
  12. Hutton CV. On approximation numbers and its adjoint. Math Ann 1974; 210: 277-280
  13. Lindenstrauss J. Extension of compact operators. Mem Amer Math Soc 1964; 48: 1-112
  14. Lindenstrauss J, Tzafriri L. Classical Banach Spaces I, Sequence Spaces. Berlin, Germany: Springer-Verlag, 1977
  15. Nachbin L. A theorem of the Hanh Banach type for linear transformations. T Am Math Soc 1950; 68: 28-46
  16. Persson A, Pietsch P. p-Nukleare und p-integrale Abbildungen in Banachr￿umen. Studia Math 1969; 33: 19-62 (in German)
  17. Pietsch P. Approximation spaces. J Approx Theory 1981; 32: 115-134
  18. Randtke DJ. Representation theorems for compact operators. P Am Math Soc 1973; 37: 481-485
  19. Sofi MA. A note on embedding into product spaces. Czechoslovak Math J 2006; 56: 507-513
  20. Terzioğlu T. A characterization of compact linear mappings. Arch Math 1971; 22: 76-78
  21. Terzioğlu T. Remarks on compact and infinite-nuclear mappings. Mathematica Balkanica 1972; 2: 251-255
  22. Yosida K. Functional Analysis. Berlin, Germany: Springer-Verlag, 1965.