extend numerical radius for adjointable operators on Hilbert C^* -modules
Subject Areas : StatisticsM. Shah Hosseini 1 , B. MOOSAVI 2
1 - Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Safadasht Branch, Islamic Azad Univer-
sity, Tehran, Iran.
Keywords: عملگرهای خطی و کران دار, نرم عملگری, برد عددی, شعاع عددی, فضای هیلبرت 〖-C〗^*مدول,
Abstract :
In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.
[1] C. Berger, A strange dilatation theorem. Notices mer. Math. Soc.,12 (1965) 590.
[2] S. S. Dragomir, Some inequalities for the norm and the numerical radius of linear operators in Hilbert Spaces, Tamkang J. Math. 39(1) (2008), 1–7.
[3] S. S. Dragomir, Inequalities for the norm and the numerical radius of linear operators in Hilbert space, Demonstratito Math. Soc, 40(2)(2007), 411-417.
[4] K. E. Gustafson and D. K. M. Rao, Numerical range, The field of values of linear operators and matrices, Universitext. Springer-Verlag, New York, 1997.
[5] J. A. R. Holbrook, ‘Multiplicative properties of the numerical radius in operator theory’, J. reine angew. Math. 237 (1969), 166–174.
[6] F. Kittaneh, A numerical radius inequality and an estimate for the numerical radius of the Frobenius companion matrix, Studia Math. 158 (2003), 11–17.
[7] F. Kittaneh, Numerical radius inequalities for Hilbert space operator, Studia Math. 168 (2005), 73–80.
[8] F. Kittaneh, M.S. Moslehian and T. Yamazaki, Cartesian ecomposition and numerical radius inequalities, Linear Algebra Appl. 471 (2015), 46–53.
[9] E.C. Lance, Hilbert -modules, London Mathematical Society Lecture Note Series, 210, Cambridge University Press, Cambridge, 1995.
[10] M. Sattari and M.S. Moslehian, Inequalities for operator space numerical radius of block matrices, J. Math. Phys. 57 (2016), 015201, 15pp.
