Lifting properties in operator ranges

M. LAURA ARIAS; GUSTAVO CORACH; M. CELESTE GONZALEZ

ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)

University of Szeged

Año: 2009 vol. 75 p. 635 - 653

0001-6969

Given a bounded positive linear operator A on a Hilbert space H we consider the semi-Hilbertian space (H, <>_A), where <x,y>_A =< Ax, y>. On the other hand, we consider the operator range R(A^1/2) with itscanonical Hilbertian structure, denoted by R(A^1/2). In this paper we explore the relationship between different types of operators on (H, <>_A) with classical subsets of operators on R(A^1/2), like Hermitian, normal, contractions, projections, partial isometries and so on. We extend a theorem by M. G. Krein on symmetrizable operators and a result by M. Mbekhta on reduced minimum modulus.