Some Inequalities for (α,β)-Normal Operators in Hilbert Spaces

Dragomir, Sever S and Moslehian, Mohammad Sal (2007) Some Inequalities for (α,β)-Normal Operators in Hilbert Spaces. Research report collection, 10 (Supp).


An operator T is called (α,β)-normal (0 ≤ α ≤ 1 ≤ β) if α²T*T ≤ TT* ≤ β²T*T. In this paper, we establish various inequalities between the operator norm and its numerical radius of (α,β)-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.

Item type Article
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords numerical radius, bounded linear operator, Hilbert space, (α,β)-normal operator
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