Conditions that the product of operators is an EP operator in Hilbert C*-module

Abstract

The block operator matrix decomposition is used to get new conditions under which the product of two operators is EP while none of them is an EP operator, and the same technique is employed to achieve a new characterization of EP operators. The communication of classes idempotent and normal operators with other common classes of special operators, such as EP, star dagger, bi-EP, and bi dagger operators, are presented, which are derived through matrix operators and Moore–Penrose inverses of operators in the Hilbert $C^{\ast }$-module setting.

COMMUNICATED BY:

• Hwa-Long Gau

Keywords:

• Moore–Penrose inverse
• EP
• bi-EP
• Hilbert $C^{\ast }$-module

2010 Mathematics Subject Classifications:

• 47A05
• Secondary 15A09
• 46L08
• 46L05

Acknowledgments

The authors thank the referee for valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.