In:
Journal of Operator Theory, Theta Foundation, Vol. 86, No. 1 ( 2021-07-15), p. 163-188
Abstract:
We consider compact perturbations S=DΛ+K of normal diagonal operators DΛ by certain compact operators. Sufficient conditions for K to ensure the existence of non-trivial hyperinvariant subspaces for S have recently been obtained by Foia\c{s} et al. in C.\ Foia\c{s}, I.B.\ Jung, E.\ Ko, C. Pearcy, \textit{J.\ Funct. Anal.} \textbf{253}(2007), 628--646, C.\ Foia\c{s}, I.B.\ Jung, E.\ Ko, C.~Pearcy, \textit{Indiana Univ.\ Math.\ J.} \textbf{57}(2008), 2745--2760, {C.\ Foia\c{s}, I.B.\ Jung, E.\ Ko, C.Pearcy}, \textit{J.\ Math.\ Anal.\ Appl.} \textbf{375}(2011), 602--609 (followed by Fang--Xia \textit{J.\ Funct. Anal} \textbf{263}(2012), 135-1377, and Klaja \textit{J.\ Operator Theory} \textbf{73}(2015), 127--142, by using certain spectral integrals along straight lines through the spectrum of S. In this note, the authors use circular cuts and get positive results under less restrictive local conditions for K.
Type of Medium:
Online Resource
ISSN:
0379-4024
,
1841-7744
DOI:
10.7900/jot.y2021v086i01
DOI:
10.7900/jot.2020feb17.2269
Language:
Unknown
Publisher:
Theta Foundation
Publication Date:
2021
detail.hit.zdb_id:
2043904-0
SSG:
17,1
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