Korean J. Math.  Vol 27, No 1 (2019)  pp.165-173
DOI: https://doi.org/10.11568/kjm.2019.27.1.165

A note on some inequalities for the $b$-numerical radius and $b$-norm in 2-Hilbert space operators

Akram Babri Bajmaeh, Mohsen Erfanian Omidvar

Abstract


In this paper, the definition $b$-numerical radius and $b$-norm is introduced and we present several $b$-numerical radius inequalities. Some applications of these inequalities are considered as well.

Keywords


numerical radius, usual operator norm, b-numerical radius ,

Subject classification

47A12, 47A30, 47A63.

Sponsor(s)



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References


Y. J. Cho, M. Matic and J. E. Pecaric, On Grams determinant in 2-inner product (Google Scholar)

spaces, J. Korean Math. Soc, 38 (2001), No. 6, pp.1125-1156. (Google Scholar)

R.W. Freese and Y. J. Cho, Geometry of Linear 2-Normed Spaces, Nova Science Publishers, Inc, New York, 2001. (Google Scholar)

K.E. Gustafson and D. K. M. Rao, Numerical range, Springer, New York, 1997. (Google Scholar)

M. EL. Hadad, F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 182 (2007), 133-140. (Google Scholar)

P. K. Harikrishnan and K. T. Ravindran, Riesz theorems in 2-inner product spaces, Novi Sad J. Math, Vol. 41, No 2, (2011), 57-61. (Google Scholar)

F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168(1) (2005), 73-80. (Google Scholar)


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