Rotfel’d inequality for partitioned matrices with numerical ranges in a sector

Abstract

Let be a concave function and let , where and are square, be a complex matrix such that the numerical range of is contained in for . Then, we show that

for all unitarily invariant norms.

Keywords:

• concave function
• numerical range
• accretive–dissipative matrix
• unitarily invariant norm

AMS Subject Classifications:

• 47A63
• 47A30

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research was supported by the key project of the applied mathematics of Hainan Normal University, the natural science foundation of Hainan Province [grant number 114007]; Chongqing Graduate Student Research Innovation project [grant number CYS14020].