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Periodic groups of operators in Banach spaces


Author: B. Nagy
Journal: Proc. Amer. Math. Soc. 126 (1998), 1433-1444
MSC (1991): Primary 47B40, 47D03
DOI: https://doi.org/10.1090/S0002-9939-98-04298-1
MathSciNet review: 1443399
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Abstract: Spectral operators of scalar type in the sense of Dunford often occur in connection with unconditionally convergent series expansions, whereas conditionally convergent expansions under similar conditions may be described with the help of operators having a more general type of spectral decomposition. We show that under certain conditions even in the latter case we can restrict our considerations to a dense linear submanifold of the original Banach space with a stronger topology, where the convergence of the expansion under study will be unconditional. Though our conditions could be formulated in terms of a single operator, it seems to be more natural to state them in terms of (the generator of) a periodic group of operators.


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Additional Information

B. Nagy
Affiliation: Department of Analysis, Institute of Mathematics, Technical University of Budapest, H-1521 Budapest, Hungary
Email: bnagy@ch.bme.hu

DOI: https://doi.org/10.1090/S0002-9939-98-04298-1
Keywords: Periodic group of operators, spectral operator of scalar type, unconditional convergence
Received by editor(s): October 21, 1996
Additional Notes: Supported by a Hungarian NSF Grant (OTKA No. T-016925)
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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