J -Selfadjoint Krein Space Operators and Aluthge Transforms
- Authors
- An, IJ; Heo, J
- Issue Date
- May-2021
- Publisher
- Birkhauser
- Keywords
- Aluthge transform; J -selfadjoint operator; (a-)Weyl’s theorem; (a-)Browder’s theorem; J -Fredholm theory; J -Weyl spectrum; J -Browder spectrum
- Citation
- Mediterranean Journal of Mathematics, v.18, no.4, pp.1 - 16
- Indexed
- SCIE
SCOPUS
- Journal Title
- Mediterranean Journal of Mathematics
- Volume
- 18
- Number
- 4
- Start Page
- 1
- End Page
- 16
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/141928
- DOI
- 10.1007/s00009-021-01779-5
- ISSN
- 1660-5446
- Abstract
- In this paper, we give a refined polar decomposition of a J-selfadjoint operator on a Krein space by decomposing the partial isometry in the polar decomposition. Using this refined polar decomposition, we prove some relations between J-selfadjoint operators and their (s, t)-Aluthge transforms. We investigate various spectra of a J-adjoint T# and a J-adjoint T~ # of its Aluthge transform for a bounded Krein space operator T. Using their spectra, we develop Fredholm theory and J-Fredholm theory for the products T#T and TT# and their Aluthge transforms T#T~ and TT#~ , which become Fredholm, J-Fredholm, (a-)Weyl, or (a-)Browder.
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