A characterization of operators via Berezin symbol and related questions

[1]N. Aronzajn, Theory of reproducing kernels, Transactions of the American Mathematical Society, 68(1950), 337-404.Search in Google Scholar

[2]F.A. Berezin, Covariant and contravariant symbols for operators, Mathematics of the USSR-Izvestiya, 6(1972): 1117-1151.Search in Google Scholar

[3]M. Bakherad M, M. Hajmohamadi, R. Lashkaripour, S. Sahoo, Some extensions of Berezin number inequalities on operators, Rocky Mountain Journal of Mathematics, 51(2021), 1941-1951.Search in Google Scholar

[4]M.L. Buzano, Generalizzazione della disiguaglianza di Cauchy-Schwaz, Rendiconti del Seminario Matematico Università e Politecnico di Torino, 31(1971), 405-409 (in Italian).Search in Google Scholar

[5]S.S. Dragomir, Some Grüss type inequalities in inner product spaces, J. Inequal. Pure Appl. Math., 4(2)(2003), Article 42.Search in Google Scholar

[6]M. Hajmohamadi, R. Lashkaripour and M. Bakherad, Improvements of Berezin number inequalities, Linear and Multilinear Algebra, 68(2020), 1218-1229.Search in Google Scholar

[7]M.T. Garayev, H. Guediri, H. Sadraoui, Applications of reproducing kernels and Berezin symbols, New York J. Math., 22(2016), 583–604.Search in Google Scholar

[8]M.T. Garayev, M.W. Alomari, Inequalities for the Berezin number of operators and related questions, Complex Analysis and Operator Theory, 15(2021), 1-30.Search in Google Scholar

[9]M.T. Karaev, Berezin symbol and invertibility of operators on the functional Hilbert spaces, Journal of Functional Analysis, 238(2006), 181-192.Search in Google Scholar

[10]M.T. Karaev, Reproducing kernels and Berezin symbols techniques in various questions of operator theory, Complex Analysis and Operator Theory, 7(2013), 983-1018.Search in Google Scholar

[11]F. Kittaneh, Notes on some inequalities for Hilbert space operators, Publications of the Research Institute for Mathematical Sciences, 24(1988), 283-293.Search in Google Scholar

[12]S. Sahoo, N. Das and N.C. Rout, On Berezin number inequalities for operator matrices, Acta Mathematica Sinica English Series, 37(2021), 873-892.Search in Google Scholar

[13]S. Saitoh and Y. Sawano, Theory of Reproducing Kernels and Applications, Singapore: Springer, 2016.Search in Google Scholar

[14]S. Saltan, On the weak limit of compact operators on the reproducing kernel Hilbert space and related questions, Analele Universitatii Ovidius Constanta. Seria Matematica, 24(2016), 253-260.Search in Google Scholar

[15]R. Tapdigoglu, New Berezin symbol inequalities for operators on the reproducing kernel Hilbert space, Operators and Matrices, 15(2021), 1031-1043.Search in Google Scholar

[16]U. Yamancı, R. Tunç and M. Gürdal, Berezin number, Grüss-type inequalities and their applications, Bulletin of the Malaysian Mathematical Sciences Society, 43(2020), 2287-2296.Search in Google Scholar

[17]U. Yamancı and İ.M. Karlı, Further refinements of the Berezin number inequalities on operators, Linear and Multilinear Algebra, 70(2022), 5237-5246.Search in Google Scholar

[18]U. Yamancı, On the summability methods of logarithmic type and the Berezin symbol, Turkish Journal of Mathematics, 42(2018), 2417-2422.Search in Google Scholar

[19]K. Zhu, Operator theory in function spaces. Second ed., Mathematical Surveys and Monographs, Vol. 138, American Mathematical Society, Providence, R.I. 2007.Search in Google Scholar