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.)
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