Abstract
Given any complex matrix, and consider it as an operator. The purpose of this paper is to given an upper bound for this operator. Our results not only generalize Bennett [Be 1], but also improve Bennett [Be 2] [Be 3], and Borwein-Cass [BC]. 1.Introduction…………………………………………1 2.Preliminaries………………………………………7 3.Proofs of Main Results…………………………10 4.The Results From Adjoint………………………12 5.A Partial Solution to Bennett’s Problem……15 References………………………………………………17