ACTA issues

Partial isometries and generalized inverses

Mostafa Mbekhta

Acta Sci. Math. (Szeged) 70:3-4(2004), 767-781

Abstract. In the present paper we establish that a contraction on a Hilbert space is a partial isometry if and only if it has a contractive generalized inverse. An equivalent characterization is that its reduced minimum modulus is greater than or equal to $1$. The first equivalence enables us to define a partial isometry in the more general context of Banach spaces.

AMS Subject Classification (1991): 47A53, 47A68, 46B04

Keyword(s): partial isometry, generalized inverse, minimum modulus, reduced minimum modulus

Received February 24, 2004, and in final form June 8, 2004. (Registered under 5844/2009.)