ACTA issues

On the Cauchy dual of closed range operators

H. Ezzahraoui, M. Mbekhta, E. H. Zerouali

Acta Sci. Math. (Szeged) 85:1-2(2019), 231-248

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.)