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Lorentz-Schatten classes of direct sum of operators

Year 2020, Volume: 49 Issue: 2, 835 - 842, 02.04.2020
https://doi.org/10.15672/hujms.522814

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.

References

  • [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.
Year 2020, Volume: 49 Issue: 2, 835 - 842, 02.04.2020
https://doi.org/10.15672/hujms.522814

Abstract

References

  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Pembe Ipek Al 0000-0002-6111-1121

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Ipek Al, P. (2020). Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics, 49(2), 835-842. https://doi.org/10.15672/hujms.522814
AMA Ipek Al P. Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):835-842. doi:10.15672/hujms.522814
Chicago Ipek Al, Pembe. “Lorentz-Schatten Classes of Direct Sum of Operators”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 835-42. https://doi.org/10.15672/hujms.522814.
EndNote Ipek Al P (April 1, 2020) Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics 49 2 835–842.
IEEE P. Ipek Al, “Lorentz-Schatten classes of direct sum of operators”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 835–842, 2020, doi: 10.15672/hujms.522814.
ISNAD Ipek Al, Pembe. “Lorentz-Schatten Classes of Direct Sum of Operators”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 835-842. https://doi.org/10.15672/hujms.522814.
JAMA Ipek Al P. Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics. 2020;49:835–842.
MLA Ipek Al, Pembe. “Lorentz-Schatten Classes of Direct Sum of Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 835-42, doi:10.15672/hujms.522814.
Vancouver Ipek Al P. Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):835-42.