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- Title
Localizable spectrum and bounded local resolvent functions.
- Authors
Vladimir Müller; Michael Neumann
- Abstract
Abstract. Given a Banach space operator with interior points in the localizable spectrum and without non-trivial divisible subspaces, this article centers around the construction of an infinite-dimensional linear subspace of vectors at which the local resolvent function of the operator is bounded and even admits a continuous extension to the closure of its natural domain. As a consequence, it is shown that, for any measure with natural spectrum on a locally compact abelian group, the corresponding operator of convolution on the group algebra admits a non-zero bounded local resolvent function precisely when its spectrum has non-empty interior.
- Subjects
MATHEMATICAL analysis; COMPLEX variables; BANACH spaces; MATHEMATICS
- Publication
Archiv der Mathematik, 2008, Vol 91, Issue 2, p155
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-008-2652-6