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- W2951570080 abstract "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 $x_iin H^*_A$ and a non-increasing sequence of eigenvalues $lambda_iin A$ such that $K,x_i = x_i,lambda_i$ and the autodual Hilbert $A$-module generated by these eigenvectors is the whole $H_A^*$. As an application we consider the Schrodinger operator in magnetic field with irrational magnetic flow as an operator acting in a Hilbert module over the irrational rotation algebra $A_{theta}$ and discuss the possibility of its diagonalization." @default.
- W2951570080 created "2019-06-27" @default.
- W2951570080 creator A5077262657 @default.
- W2951570080 date "1994-12-16" @default.
- W2951570080 modified "2023-09-27" @default.
- W2951570080 title "Diagonalization of compact operators in Hilbert modules over finite W*-algebras" @default.
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