A note on the star order in Hilbert spaces |
| |
| Authors: | J Antezana C Cano I Mosconi D Stojanoff |
| |
| Institution: | 1. Instituto Argentino de Matemática, CONICET , Buenos Aires, Argentina;2. Departament de Matemàtiques , Universitat Autònoma de Barcelona , Barcelona, Spain jaantezana@mat.uab.cat;4. Departamento de Matemática (FCE) , Universidad Nacional del Comahue , Neuquén, Argentina;5. Departamento de Matemática , Universidad Nacional de La Plata , La Plata, Argentina |
| |
| Abstract: | We study the star order on the algebra L(?) of bounded operators on a Hilbert space ?. 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. |
| |
| Keywords: | star order projections functional calculus polar decomposition semi-lattice structure shorted operators |
|
|
