SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 2

Lorentz-Schatten classes of direct sum of operators

Pembe Ipek Al(Karadeniz Technical University)0000-0002-6111-1121
Pages
—
Publication Date
2020-04-02
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Then, the results are supported by applications.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the relations between Lorentz-Schatten property of the direct sum of operators and Lorentz-Schatten property of its coordinate operators are studied.
📊
Key Findings & Data:In this paper, the relations between Lorentz-Schatten property of the direct sum of operators and Lorentz-Schatten property of its coordinate operators are studied.
💡
Conclusion & Impact:Then, the results are supported by applications.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:direct sum of Hilbert spaces and operators · compact operators · Lorentz-Schatten operator classes

Abstract

In this paper, the relations between Lorentz-Schatten property of the direct sum of operators and Lorentz-Schatten property of its coordinate operators are studied. Then, the results are supported by applications.

🔖

Cite This Article

Al, P. I. (2020). Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 2. https://doi.org/10.15672/hujms.522814

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. M.Sh. Birman and M.Z. Solomyak, Estimates of singular numbers of integral operators, Russian Math. Survey 32 (1), 15-89, 1977 (Translated from Uspekhi Mat. Nauk 32 (1), 17-84, 1977).
  2. I. Chalendar, E. Fricain, M. Gürdal and M. T. Karaev, Compactness and Berezin symbols, Acta Sci. Math. (Szeged) 78 (1), 315-329, 2012.
  3. F. Cobos, D.D. Haroske, T. Kühn and T. Ullrich, Mini-workshop: modern applications of s-numbers and operator ideals, Mathematisches Forschungs Institute Oberwolfach, Germany, 369-397, 8-14 February 2015.
  4. N. Dunford and J.T. Schwartz, Linear Operators I, Interscience Publishers, 1958.
  5. I.C. Gohberg and M.G. Krein, Introduction to the Theory of Linear Non-Selfadjoint Operators in Hilbert Space, American Mathematical Society, 1969.
  6. Z.I. Ismailov, Compact inverses of first-order normal differential operators, J. Math. Anal. Appl. 320, 266-278, 2006.
  7. Z.I. Ismailov, Multipoint normal differential operators for first order, Opuscula Math. 29, 399-414, 2009.
  8. Z.I. Ismailov, E. Otkun Çevik and E. Unluyol, Compact inverses of multipoint normal differential operators for first order, Electron. J. Differential Equations 89, 1-11, 2011.
  9. Z.I. Ismailov and E. Unluyol, Hyponormal differential operators with discrete spectrum, Opuscula Math. 30, 79-94, 2010.
  10. M.T. Karaev, M. Gürdal and U. Yamancı, Special operator classes and their properties, Banach J. Math. Anal. 7 (2), 74-88, 2013.
  11. M.A. Naimark and S.V. Fomin, Continuous direct sums of Hilbert spaces and some of their applications, Uspehi Mat. Nauk 10, 111-142, 1955, (in Russian).
  12. E. Otkun Çevik and Z.I. Ismailov, Spectrum of the direct sum of operators, Electron. J. Differential Equations 210, 1-8, 2012.
  13. A. Pietsch, Operators Ideals, North-Holland Publishing Company, 1980.
  14. A. Pietsch, Eigenvalues and s-Numbers, Cambridge University Press, 1987.
  15. R. Schatten and J. von Neumann, The cross-space of linear transformations, Ann. of Math. 47, 608-630, 1946.
  16. E. Schmidt, Zur theorie der linearen und nichtlinearen integralgleichungen, Math. Ann. 64, 433-476, 1907.
  17. H. Triebel, Über die verteilung der approximationszahlen kompakter operatoren in Sobolev-Besov-Raumen, Invent. Math. 4, 275-293, 1967.