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On quasispectral maximal subspaces
of a class of Volterra-type operators

Author: Roman Drnovsek
Journal: Proc. Amer. Math. Soc. 125 (1997), 1081-1087
MSC (1991): Primary 47B38, 47A15
MathSciNet review: 1363455
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Abstract: The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladi\v{c} in 1984. As an application a class of quasinilpotent operators on $L^p$-spaces, close to the Volterra kernel operator, was studied. In the present Banach function space setting we determine all quasispectral maximal subspaces of analogues of such operators and prove that these subspaces are all the invariant bands. An example is given showing that (in general) they are not all the closed, invariant ideals of the operator.

References [Enhancements On Off] (What's this?)

  • 1. Matjaž Omladič, Quasispectral subspaces of quasinilpotent operators, Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), no. 3-4, 349–354. MR 768355, 10.1017/S0308210500013512
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Additional Information

Roman Drnovsek
Affiliation: Institute of Mathematics, Physics and Mechanics Jadranska 19, 1000 Ljubljana, Slovenia

Keywords: Banach function spaces, operators, invariant subspaces
Received by editor(s): July 6, 1995
Received by editor(s) in revised form: September 22, 1995
Additional Notes: This work was supported in part by the Research Ministry of Slovenia.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society