Abstract. We extend in this paper the notion of Cauchy dual to operators with closed range. We then give several useful properties of Cauchy duals extending the case of left-invertible operators. As a consequence, we show that a weak concavity concept of an operator induces a corresponding weak hyponormality of its Cauchy dual.

DOI: 10.14232/actasm-018-020-2

AMS Subject Classification (1991): 47B20

Keyword(s): closed range, hyperexpansive operators, Cauchy dual, Moore--Penrose inverse

Received February 10, 2018 and in final form June 28, 2018. (Registered under 20/2018.)