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

Sungeun Jung; Eungil Ko

doi:10.1112/blms/bdt008

Subscalarity of operators for which TT and T + T commute

Sungeun Jung, Eungil Ko

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	849-860
Number of pages	12
Journal	Bulletin of the London Mathematical Society
Volume	45
Issue number	4
DOIs	https://doi.org/10.1112/blms/bdt008
State	Published - 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).

Access to Document

10.1112/blms/bdt008

Cite this

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