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Periodic groups of operators in Banach spaces
Author(s):
B.
Nagy
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1433-1444.
MSC (1991):
Primary 47B40, 47D03
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.
References:
- [Bad]
- W.G.Bade, On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc., 80 (1955), 345-360. MR 17:513d
- [BBG]
- H.Benzinger, E.Berkson and T.A.Gillespie, Spectral families of projections, semigroups and differential operators, Trans. Amer. Math. Soc., 275 (1983), 431-475. MR 84b:47038
- [BP]
- A.Brown and C.Pearcy, Introduction to operator theory I: Elements of functional analysis, Springer, New York, 1977. MR 58:23463
- [Dav]
- E.B.Davies, One-parameter semigroups, Academic Press, London, 1980. MR 82i:47060
- [DS]
- N.Dunford and J.T.Schwartz, Linear operators, Part I: General theory,Wiley, New York, 1958. Part III: Spectral operators, Wiley-Interscience, New York, 1971. MR 22:8302; MR 54:1009
- [E1]
- R.E.Edwards, Fourier series: A modern introduction, Vol. 2, 2nd ed., Springer, New York, 1982. MR 83k:42001
- [E2]
- R.E.Edwards, Functional analysis, Holt, Rinehart and Winston, New York, 1965. MR 36:4308
- [Gar]
- J.B.Garnett, Bounded analytic functions, Academic Press, New York, 1981. MR 83g:30037
- [HP]
- E.Hille and R.S.Phillips, Functional analysis and semi-groups, Amer. Math. Soc., Providence, 1957. MR 19:664d
- [K1]
- S.Kantorovitz, The semi-simplicity manifold of arbitrary operators, Trans. Amer. Math. Soc., 123 (1966), 241-252. MR 33:572
- [K2]
- S.Kantorovitz, Spectrality criteria for unbounded operators with real spectrum, Math. Ann., 256 (1981), 19-28. MR 82i:47049
- [KH]
- S.Kantorovitz and R.J.Hughes, Spectral representations for unbounded operators with real spectrum, Math. Ann., 282 (1988), 535-544. MR 90a:47009
- [McC]
- C.A.McCarthy, Commuting Boolean algebras of projections I, Pacific J. Math., 11 (1961), 295-307. MR 23:A2750
- [Nag]
- R.Nagel (ed.) et al., One-parameter semigroups of positive operators, Springer, Berlin, 1986. MR 88i:47022
- [Orl]
- W.Orlicz, Beiträge zur Theorie der Orthogonalentwicklungen II, Studia Math., 1 (1929), 241-255.
- [RSz]
- F.Riesz and B.Sz.-Nagy, Lecons d'analyse fonctionnelle, Acad. Sci. Hong., Budapest, 1952. MR 14:286d
- [Sma]
- D.R.Smart, Some examples of spectral operators, Illinois J. Math., 11 (1967), 603-607. MR 36:724
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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:
10.1090/S0002-9939-98-04298-1
PII:
S 0002-9939(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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