Every Operator Almost Commutes with a Compact Operator

In this note we set forth three possible definitions of the property of "almost commuting with a compact operator" and discuss an old result of W. Arveson that says that every operator on Hilbert space has the weakest of the three properties. Finally, we discuss some recent progress on the...

Full description

Saved in:
Bibliographic Details
Published inKyungpook mathematical journal Vol. 47; no. 2; pp. 221 - 226
Main Authors Jung, Il Bong, Ko, Eungil, Pearcy, Carl
Format Journal Article
LanguageKorean
Published 2007
Subjects
hyperinvariant subspace
invariant subspace
compact operator
Online AccessGet full text

Cover

More Information
Summary:In this note we set forth three possible definitions of the property of "almost commuting with a compact operator" and discuss an old result of W. Arveson that says that every operator on Hilbert space has the weakest of the three properties. Finally, we discuss some recent progress on the hyperinvariant subspace problem (see the bibliography), and relate it to the concept of almost commuting with a compact operator.
Bibliography:KISTI1.1003/JNL.JAKO200736135723288
ISSN:1225-6951
0454-8124