info:eu-repo/semantics/article
Lifting properties in operator ranges
Fecha
2009-01Registro en:
Arias, Maria Laura; Corach, Gustavo; Gonzalez, Maria Celeste; Lifting properties in operator ranges; University of Szeged; Acta Scientiarum Mathematicarum (Szeged); 75; 3; 1-2009; 635-653
0001-6969
CONICET Digital
CONICET
Autor
Arias, Maria Laura
Corach, Gustavo
Gonzalez, Maria Celeste
Resumen
Given a bounded positive linear operator A on a Hilbert space H we consider the semi-Hilbertian space (H, <,>_A), where <ℇ, n >_A =< Aℇ,n>. On the other hand, we consider the operator range R(A^1/2) with its canonical 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.