Bounds for the p‐Numerical Radius Through Singular Values

Abstract

In this paper, we prove some bounds for the ‐numerical radius as natural extensions of certain known bounds for the numerical radius. This complements many recent studies in this direction.

Among many results, we show that if is an complex matrix, with Aluthge transform , then for , where and denote the ‐numerical radius and the Schatten ‐norm, respectively. This extends a celebrated result by Yamazaki, who showed the same result when .