FURTHER BEREZIN NUMBER INEQUALITIES OF OPERATOR MATRICES

Messaoud Guesba, Ulas Yamanci

DOI Number
https://doi.org/10.22190/FUMI221014034G
First page
519
Last page
533

Abstract


In this paper, we have some inequalities for the Berezin number of operator matrices using the convex functions. Also, we obtain some upper bounds for the Berezin number of operator matrices. These results improve some earlier related Berezin number inequalities.


Keywords

Berezin number, Berezin norm, reproducing kernel Hilbert space, operator matrices.

Full Text:

PDF

References


bibitem {Abu}A. Abu-Omar, F. Kittaneh, Numerical radius inequalities for

$ntimes n$ operator matrices, textit{Linear Algebra Appl.} textbf{468}

(2015) 18-26.

bibitem {AL}M. Al-Dolat, I. Jaradat, B. Al-Husban, A novel numerical radius

upper bounds for $2times2$ operator matrices, textit{Linear Multilinear

Algebra} textbf{70}(6)(2022) 1173-1184.

bibitem {Bak01}M. Bakherad, M. Hajmohamadi, R. Lashkaripour, S. Sahoo, Some

extensions of Berezin number inequalities on operators, textit{Rocky Mountain

J. Math}, textbf{51}(6)(2021) 1941-1951

bibitem {Bak1}M. Bakherad, R. Lashkaripour, M. Hajmohamadi, U. Yamanci,

Complete refinements of the Berezin number inequalities, textit{J. Math.

Inequal.} textbf{4}(13)(2019) 1117-1128.

bibitem {Bak2}M. Bakherad, M.T. Garayev, Berezin number inequalities for

operators, textit{Concr. Oper.} textbf{6}(2019) 33-43.

bibitem {Bak3}M. Bakherad, K. Shebrawi, Upper bounds for numerical radius

inequalities involving off-diagonal operator matrices, textit{Ann. Funct.

Anal.} textbf{9}(3)(2018) 297-309.

bibitem {Bak4}M. Bakherad, Some Berezin number inequalities for operator

matrices, textit{Czechoslovak Math. J.} textbf{68}(4)(2018) 997-1009.

bibitem {BA}W. Bani-Domi, F. Kittaneh, Norm and numerical radius inequalities

for Hilbert space operators, textit{Linear Multilinear Algebra}

textbf{69}(5)(2021) 934-945.

bibitem {ber1}F.A. Berezin, Covariant and contravariant symbols for

operators, textit{Math. USSR-Izv.} textbf{6} (1972) 1117-1151.

bibitem {BH}P. Bhunia, K. Paul, A. Sen, Inequalities involving Berezin norm

and Berezin number, textit{Complex Anal. Oper. Theory} textbf{17}(7)(2023) 1-17.

bibitem {BU}M.L. Buzano, Generalizzazione della diseguaglianza di

Cauchy-Schwarz, (Italian), textit{Rend. Sem. Mat. Univ.e Politech. Torino}

textbf{31} (1974) 405-409.

bibitem {cas}L.P. Castro, S. Saitoh, Numerical solutions of linear singular

integral equations by means of Tikhonov regularization and reproducing

kernels, textit{Houston J. Math.} textbf{38}(4)(2012) 1261-1276.

bibitem {cas2}L.P. Castro, S. Saitoh, Y. Sawano, A.M. Simoes, General

inhomogeneous discrete linear partial differential equations with constant

coefficients on the whole spaces, textit{Complex Anal. Oper. Theory}

textbf{6}(1)(2012) 307-324.

bibitem {D}S.S. Dragomir, Power inequalities for the numerical radius of a

product of two operators in Hilbert spaces, textit{Sarajevo J. Math.}

textbf{5}(2009) 269-278.

bibitem {G}K.E. Gustafson, D.K.M. Rao, Numerical range, New York: Springer; 1997.

bibitem {HA}M. Hajmohamadi, R. Lashkaripour, M. Bakherad, Improvements of

Berezin number inequalities, textit{Linear Multilinear Algebra}

textbf{68}(6)(2020) 1218-1229.

bibitem {H}J.C. Hou, H.K. Du, Norm inequalities of positive operator

matrices, textit{Integr. Equ. Oper. Theory} textbf{22}(1995) 281-294.

bibitem {Kar0}M.T. Karaev, Berezin symbol and invertibility of operators on

the functional Hilbert spaces, textit{J. Funct. Anal.} textbf{238} (2006) 181-192.

bibitem {Kar}M.T. Karaev, Reproducing kernels and Berezin symbols techniques

in various questions of operator theory, textit{Complex Anal. Oper. Theory}

textbf{7} (2013) 983-1018.

bibitem {K0}F. Kittaneh, Notes on some inequalities for Hilbert space

operators, textit{Publ. RIMS Kyoto Univ.} textbf{24}(1988) 283-293.

bibitem {K}F. Kittaneh, Numerical radius inequalities for Hilbert space

operators., textit{Stud. Math.} textbf{168}(2005) 73-80.

bibitem {K1}F. Kittaneh, Spectral radius inequalities for Hilbert space

operators, Proc. Amer. Math. Soc., 134 (2006), 385-390.

bibitem {M}B. Mond, J. Pecaric, On Jensen's inequality for operator convex

functions, textit{Houston J. Math.}, textbf{21}(1995) 739-753.

bibitem {fil}H. Moradi, M. Sababheh, New estimates for the numerical radius,

Filomat, 35(14)(2021), 4957-4962.

bibitem {MO}H.R. Moradi, S. Furuichi, F.C. Mitroi, R. Naseri, An extension of

Jensen's operator inequality and its application to Young inequality,

textit{Rev. R. Acad. Cienc. Exact. Fs. Nat. Ser. A Mat.} textbf{113}(2019) 605-614.

bibitem {P}V.I. Paulsen, M. Raghupati, An introduction to the theory of

reproducing kernel Hilbert spaces, Cambridge Univ. Press, 2016.

bibitem {sss}S. Sahoo, N. Das, N.C. Rout, On Berezin number inequalities for

operator matrices, textit{Acta. Math. Sin.-English Ser.} textbf{37}(2021) 873-892.

bibitem {SA}S. Sahoo, N.C. Rout, New upper bounds for the numerical radius of

operators on Hilbert spaces, textit{Adv. Oper. Theory} textbf{7}(50)(2022) 1-20.

bibitem {S}K. Shebrawi, Numerical radius inequalities for certain $2times2$

operator matrices II. textit{Linear Algebra Appl.} textbf{523}(2017) 1-12.

bibitem {UM}U. Yamanci, M.T. Garayev, Some results related to the Berezin

number inequalities, textit{Turkish J. Math.} textbf{43}(4)(2019), 1940-1952.

bibitem {GU}U. Yamanci, M. Guesba, Refinements of some Berezin number

inequalities and related questions, textit{J. Anal.} textbf{31}(1)(2023) 539-549.

bibitem {zhu}K. Zhu, Operator theory in function spaces, Second edition.

Mathematical Surveys and Monographs, 138. American Mathematical Society,

Providence R.I., 2007.




DOI: https://doi.org/10.22190/FUMI221014034G

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)