On quasispectral maximal subspaces of a class of Volterra-type operators
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- by Roman Drnovsek PDF
- Proc. Amer. Math. Soc. 125 (1997), 1081-1087 Request permission
Abstract:
The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladič 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
- Matjaž Omladič, Quasispectral subspaces of quasinilpotent operators, Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), no. 3-4, 349–354. MR 768355, DOI 10.1017/S0308210500013512
- J. R. Ringrose, Compact non-self-adjoint operators, London: Van Nostrand Reinhold Math. Studies 1971
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039, DOI 10.1007/978-3-642-65970-6
- A. C. Zaanen, Riesz spaces. II, North-Holland Mathematical Library, vol. 30, North-Holland Publishing Co., Amsterdam, 1983. MR 704021, DOI 10.1016/S0924-6509(08)70234-4
Additional Information
- Roman Drnovsek
- Affiliation: Institute of Mathematics, Physics and Mechanics Jadranska 19, 1000 Ljubljana, Slovenia
- Email: roman.drnovsek@fmf.uni-lj.si
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1081-1087
- MSC (1991): Primary 47B38, 47A15
- DOI: https://doi.org/10.1090/S0002-9939-97-03660-5
- MathSciNet review: 1363455