Continuous functions of Hermitian operators

Theorem: every normal operator is a continuous function of a Hermitian one. Corollary: every normal operator on a separable Hilbert space is the sum of a diagonal operator and a compact one.

Saved in:
Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1972-01, Vol.31 (1), p.130-132
Main Author: Halmos, P. R.
Format: Article
Language:English
Subjects:
Continuous functions
Geometric planes
Hilbert spaces
Logical proofs
Mathematical functions
Mathematical theorems
Mathematics
Normal operators
Research article
Separable spaces
Topological theorems
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Theorem: every normal operator is a continuous function of a Hermitian one. Corollary: every normal operator on a separable Hilbert space is the sum of a diagonal operator and a compact one.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1972-0288617-1