Numerical radius and product of elements in C*-algebras

Abstract

Let v(a) be the numerical radius of an element a in a unital -algebra . In this paper, we show that for all if and only if . We also show that for all if and only if a is a unitary element in the centre of . Furthermore, for two fixed elements a and b in , we investigate when for all , and derive a number of consequences.

Keywords:

• Numerical range
• numerical radius
• -algebras
• unitary elements
• central elements
• states

AMS Subject Classifications:

• Primary: 47A12
• Secondary: 46L05
• 47A10

Acknowledgements

The authors thank the anonymous referee for his/her remarks and comments.

Notes

No potential conflict of interest was reported by the authors.