In:
Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), Vol. 38, No. 2 ( 1995-06), p. 313-329
Abstract:
For a pair of continuous linear operators T and S on complex Banach spaces X and Y , respectively, this paper studies the local spectral properties of the commutator C ( S, T ) given by C ( S, T )( A ): = SA − AT for all A ∈ L ( X, Y ). Under suitable conditions on T and S , the main results provide the single valued extension property, a description of the local spectrum, and a characterization of the spectral subspaces of C ( S, T ), which encompasses the closedness of these subspaces. The strongest results are obtained for quotients and restrictions of decomposable operators. The theory is based on the recent characterization of such operators by Albrecht and Eschmeier and extends the classical results for decomposable operators due to Colojoară, Foiaş, and Vasilescu to considerably larger classes of operators. Counterexamples from the theory of semishifts are included to illustrate that the assumptions are appropriate. Finally, it is shown that the commutator of two super-decomposable operators is decomposable.
Type of Medium:
Online Resource
ISSN:
0013-0915
,
1464-3839
DOI:
10.1017/S0013091500019106
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1995
detail.hit.zdb_id:
1465484-2
SSG:
17,1
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