IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Lifting properties in operator ranges
Autor/es:
MAR√ćA LAURA ARIAS, GUSTAVO CORACH, MARIA CELESTE GONZALEZ
Revista:
ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)
Editorial:
BOLYAI INSTITUTE, UNIVERSITY OF SZEGED
Referencias:
Lugar: Budapest; Año: 2009 vol. 75 p. 635 - 635
ISSN:
0001-6969
Resumen:
Given a bounded positive linear operator $A$ on a Hilbert space $\cH$ we consider the semi-Hilbertian space  $(\cH, \pint{ \ , \ }_A)$, where $\pint{ \xi , \eta}_A= \pint{A\xi, \eta}$. On the other hand, we consider the operator range $R(A^{1/2})$ with its canonical Hilbertian structure, denoted by $\R$. In this paper we explore the relationship between different types of operators on $(\cH, \pint{ \ , \ }_A)$  with classical subsets of operators on $\R$, 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.