Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 835 - 842 2020-04-02

Lorentz-Schatten classes of direct sum of operators

Pembe IPEK AL [1]


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.
direct sum of Hilbert spaces and operators, compact operators, Lorentz-Schatten operator classes
  • [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.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-6111-1121
Yazar: Pembe IPEK AL (Sorumlu Yazar)
Kurum: Karadeniz Technical University
Ülke: Turkey


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms522814, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {835 - 842}, doi = {10.15672/hujms.522814}, title = {Lorentz-Schatten classes of direct sum of operators}, key = {cite}, author = {IPEK AL, Pembe} }
APA IPEK AL, P . (2020). Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 835-842 . DOI: 10.15672/hujms.522814
MLA IPEK AL, P . "Lorentz-Schatten classes of direct sum of operators". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 835-842 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/522814>
Chicago IPEK AL, P . "Lorentz-Schatten classes of direct sum of operators". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 835-842
RIS TY - JOUR T1 - Lorentz-Schatten classes of direct sum of operators AU - Pembe IPEK AL Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.522814 DO - 10.15672/hujms.522814 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 835 EP - 842 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.522814 UR - https://doi.org/10.15672/hujms.522814 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Lorentz-Schatten classes of direct sum of operators %A Pembe IPEK AL %T Lorentz-Schatten classes of direct sum of operators %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.522814 %U 10.15672/hujms.522814
ISNAD IPEK AL, Pembe . "Lorentz-Schatten classes of direct sum of operators". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 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. 2020; 49(2): 835-842.
Vancouver IPEK AL P . Lorentz-Schatten classes of direct sum of operators. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 842-835.