Berezin symbol inequalities via Grüss type inequalities and related questions

Berezin symbol inequalities via Grüss type inequalities and related questions

We prove some new inequalities for Berezin symbols of operators via classical Grüss type inequalities. Some other related questions are also discussed.

___

  • [1] Aronzajn, N, Theory of reproducing kernels. Transactions of the American Mathematical Society 1950; 68: 337-404.
  • [2] Berezin, FA, Covariant and contravariant symbols for operators. Mathematics of the USSR-Izvestiya 1972; 6: 1117- 1151.
  • [3] Berezin, FA, Quantization, Mathematics of the USSR-Izvestiya 1974; 8: 1109-1163.
  • [4] Dragomir, SS, Quasi Grüss type inequalities for continous functions of self-adjoint operators in Hilbert spaces. Filomat 2013; 27 (2): 277-289.
  • [5] Dragomir, SS, A generalization of Grüss inequality in inner product spaces and applications. Journal of Mathematical Analysis and Applications 1999; 237: 74-82.
  • [6] Dragomir, SS, Advances in Inequalities of the Schwarz, Grüss and Bessel type in inner product spaces. Nova Science Publishers, New York, 2005.
  • [7] Dragomir, SS, Advances in Inequalities of the Schwarz, triangle and Heisenberg type in inner product spaces. Nova Science Publishers, New York, 2007.
  • [8] Dragomir, SS, Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces. Journal of Inequalities in Pure and Applied Mathematics 2004; 50 (3): Article 76..
  • [9] Engliś, M, Toeplitz operators and the Berezin transform on $H^2$ , Linear Algebra and its Applications 1995; 223/224: 171-204.
  • [10] Furuta, T, Micic Hot, J, Pecaric, J, Seo, Y, Mond Pecaric method in operator inequalities; inequalities for bounded selfadjoint operators on a Hilbert space, Element, Zagreb, 2005.
  • [11] Karaev, MT, Reproducing kernels and Berezin symbols techniques in various questions of operator theory. Complex Analysis and Operator Theory 2013; 7: 983-1018.
  • [12] Kılıç, S, The Berezin symbol and multipliers of functional Hilbert spaces. Proceedings of the American Mathematical Society 1995; 123: 3687-3691.
  • [13] Mitrinovic, DS, Pecaric, JE, Fink, AM, Classical and new inequalities in analysis, Kluwer Academic Publishers, Dordrecht, 1993.
  • [14] Nordgren, E, Rosenthal, P, Boundary values of Berezin symbols, operator theory: Advances and applications, 1994; 73: 362-368.
  • [15] Otachel, Z, On reverse Schwarz, Bessel, Grüss and Hadamard inequalities in inner product spaces. Linear and Multilinear Algebra 2020; 68: 805-827