Diagonalization of compact operators in Hilbert modules over finite W*-algebras
| dc.creator | Manuilov, V. M. | |
| dc.date | 1994-12-16 | |
| dc.date | 1995-01-11 | |
| dc.date.accessioned | 2026-07-07T08:59:16Z | |
| dc.date.available | 2026-07-07T08:59:16Z | |
| dc.description | It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of the present paper is to generalize this fact for a finite W*-algebra $A$ not necessarily commutative. We prove that for a compact operator $K$ acting in the right Hilbert $A$-module $H^*_A$ dual to $H_A$ under slight restrictions one can find a set of "eigenvectors" $x_i\in H^*_A$ and a non-increasing sequence of "eigenvalues" $λ_i\in A$ such that $K\,x_i = x_i\,λ_i$ and the autodual Hilbert $A$-module generated by these "eigenvectors" is the whole $H_A^*$. As an application we consider the Schrödinger operator in magnetic field with irrational magnetic flow as an operator acting in a Hilbert module over the irrational rotation algebra $A_θ$ and discuss the possibility of its diagonalization. | |
| dc.description | 24 pages, LaTeX, version 2.09, no figures | |
| dc.identifier | https://arxiv.org/abs/funct-an/9412004 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9412004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147650 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Diagonalization of compact operators in Hilbert modules over finite W*-algebras | |
| dc.type | text |