Every operator almost commutes with a compact operator

Il Bong Jung, Eungil Ko, Carl Pearcy

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)221-226
Number of pages6
JournalKyungpook Mathematical Journal
Issue number2
StatePublished - Jun 2007


  • Compact operator
  • Hyperinvariant subspace
  • Invariant subspace


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