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Uniformly bounded projections and semi-groups of operators

Published online by Cambridge University Press:  24 October 2008

G. O. Okikiolu
G. O. Okikiolu
Affiliation:
O.S.I.O. 23, Mile End Road, Norwich, NOR 83E
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Extract

Classes of operators called uniformly bounded projections defined on Banach spaces have been formally introduced (see for example (2), 8·9·28; 8·9·92), and their connexions with semi-groups of operators considered. Notable cases of such operators include the Dirichlet integrals which are connected with the semi-group of Poisson operators in Lp In the main conclusions of this paper, there is an exposition of the connexion between classes of uniformly bounded projections and semi-groups of operators. In particular, it is shown that certain uniformly bounded analytic semi-groups of operators give rise to classes of uniformly bounded projections. Various of the known special cases in Lp are also considered as Fourier trans form multiplier operators with characteristic functions of intervals as multipliers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 199 - 217
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Okikiolu, G. O.On the theory and applications of Dirichlet projections. J. Reine Angew. Math. 245 (1970), 149–164.Google Scholar
(2)Okikiolu, G. O.Aspects of the theory of bounded integral operators in Lp spaces (Academic Press, 1971).Google Scholar
(3)Yosida, K.Functional analysis, 2nd Edition (Springer Verlag, 1968).CrossRefGoogle Scholar