In:
Glasgow Mathematical Journal, Cambridge University Press (CUP), Vol. 36, No. 3 ( 1994-09), p. 331-343
Abstract:
Suppose that T and S are continuous linear operators on complex Banach spaces X and Y , respectively, and that A is a non-zero continuous linear mapping from X to Y . If A intertwines T and S in the sense that SA = AT , then a classical result due to Rosenblum implies that the spectra σ( T ) and σ( S ) must overlap, see [ 12 ]. Actually, Davis and Rosenthal [ 5 ]have shown that the surjectivity spectrum σ su ( T ) will meet the approximate point spectrum σ ap ( S ) in this case (terms to be denned below). Further information about the relations between the two spectra and their finer structure becomes available when the intertwiner A is injective or has dense range, see [ 9 ], [ 12 ], [ 13 ].
Type of Medium:
Online Resource
ISSN:
0017-0895
,
1469-509X
DOI:
10.1017/S0017089500030937
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1994
detail.hit.zdb_id:
1465410-6
SSG:
17,1
