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Tauberian theorems in a Banach lattice, with applications to the LP spaces

Published online by Cambridge University Press:  24 October 2008

D. C. J. Burgess
D. C. J. Burgess
Affiliation:
Magee University CollegeLondonderry
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Extract

In a previous paper (2) of the author, there was given a treatment of Tauberian theorems for Laplace transforms with values in an arbitrary Banach space. Now, in § 2 of the present paper, this kind of technique is applied to the more special case of Laplace transforms with values in a Banach lattice, and investigations are made on what additional results can be obtained by taking into account the existence of an ordering relation in the space. The general argument is again based on Widder (5) to which frequent references are made.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 242 - 249
Copyright
Copyright © Cambridge Philosophical Society 1954

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References

REFERENCES

(1)Birkhoff, G.Lattice Theory (revised ed.) (New York, 1948).Google Scholar
(2)Burgess, D. C. J.Abstract Laplace transforms and Tauberian theorems, with applications to the LP and HP classes. Proc. Lond. math. Soc. (2), 54 (1952), 94–110.CrossRefGoogle Scholar
(3)Burgess, D. C. J.Tauberian theorems for abstract Dirichlet's series, with applications to the LP spaces. Proc. Lond. math. Soc. (3), 3 (1953), 378–84.CrossRefGoogle Scholar
(4)Northcott, D. G.Abstract Tauberian theorems, with application to power series and Hilbert series. Duke Math. J. (1947), 483–502.Google Scholar
(5)Widder, D. V.The Laplace transform (Princeton, 1946).Google Scholar