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Numerical radius inequalities for finite sums of operators

Mirmostafaee A. K., Rahpeyma O. P., Omidvar M. E.

Demonstratio Mathematica

2014

Vol. 47, nr 4

963--970

In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results.

Some inequalities for the maximum of the spectrum for the real part of two operators product in Hilbert spaces

Dragomir S. S.

Demonstratio Mathematica

2010

Vol. 43, nr 3

665-680

Some inequalities for the maximum and the minimum of the spectrum for the real part of a product of two operators in Hilbert spaces are given. Applications for one operator whose transform C(...) (introduced by the author in [9]) is accretive, are given as well.

Inequalities for the numerical radius in unital normed algebras

Dragomir S.

Demonstratio Mathematica

2010

Vol. 43, nr 1

129-137

In this paper, some inequalities between the numerical radius of an element from a unital normed algebra and certain semi-inner products involving that element and the unity are given.

Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces

Dragomir S.

Demonstratio Mathematica

2007

Vol. 40, nr 2

411-417

In this paper various inequalities between the operator norm and its numerical radius are provided. For this purpose, we employ some classical inequalities for vectors in inner product spaces due to Buzano, Goldstein-Ryff-Clarke, Dragomir-Sandor and the author.