Subscalarity of operators for which T*T and T + T* commute

Sungeun Jung, Eungil Ko

Research output: Contribution to journalArticlepeer-review


In this paper, we study operators for which T*T and T + T* commute. Let Θ denote the class of such operators in L(H). We show that every operator in Θ is subscalar of order 4. From this result, we give partial solutions to the invariant subspace problem. In addition, we examine some extensions of operators in Θ. Finally, we prove that if T belongs to Θ, then Weyl's theorem holds for T and the spectral mapping theorem corresponding to the Weyl spectrum is satisfied for T.

Original languageEnglish
Pages (from-to)849-860
Number of pages12
JournalBulletin of the London Mathematical Society
Issue number4
StatePublished - Aug 2013

Bibliographical note

Funding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korean government(MEST) (2012-0000939).


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