INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
A note on the star order in Hilbert spaces
J. ANTEZANA, C. CANO, I. MOSCONI Y D. STOJANOFF
LINEAR AND MULTILINEAR ALGEBRA
TAYLOR & FRANCIS LTD
Lugar: Londres; Año: 2009
We study the star order on the algebra L(H) of bounded operators on a Hilbert space H. We present a new interpretation of this order which allows to generalize to this setting many known results for matrices: functional calculus, semi lattice properties, shorted operators and orthogonal decompositions. We also show several properties for general Hilbert spaces regarding the star order and its relationship with the functional calculus and the polar decomposition, which were unknown even in the finite dimensional setting. We also study the existence of strong limits of star-monotone sequences and nets.