Lifting properties in operator ranges

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

ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)

Año: 2008

0001-6969

Abstract 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 its canonical Hilbertian structure, denoted by RR(A^(1/2)). In this paper we explore the relationship between dierent types of operators on (H; < , >_A) with classical subsets of operators on RR(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