Operators Characterized by Certain Cauchy-Schwarz Type Inequalities

  • Hideharu Watanabe

    Kyushu University, Fukuoka, Japan

Abstract

A Hilbert space operator satisfying

is studied. The condition () defines a slightly larger class than the hyponormality, and for compact operators () is equivalent to the normality. The condition () is characterized by using an operator whose numerical radius is less than 1, and among other things we show that () and the normality are equivalent for matrices. Moreover, we show that () and the normality are equivalent for trace class operators in Appendix.

Cite this article

Hideharu Watanabe, Operators Characterized by Certain Cauchy-Schwarz Type Inequalities. Publ. Res. Inst. Math. Sci. 30 (1994), no. 2, pp. 249–259

DOI 10.2977/PRIMS/1195166132