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Positive p-summing operators, vector measures and tensor products

Published online by Cambridge University Press:  20 January 2009

Oscar Blasco
Oscar Blasco
Affiliation:
Dpto. Teoría de Funciones, Facultad de Ciencias, 50009-Zaragoza, Spain
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In this paper we shall introduce a certain class of operators from a Banach lattice X into a Banach space B (see Definition 1) which is closely related to p-absolutely summing operators defined by Pietsch [8].

These operators, called positive p-summing, have already been considered in [9] in the case p = 1 (there they are called cone absolutely summing, c.a.s.) and in [1] by the author who found this space to be the space of boundary values of harmonic B-valued functions in .

Here we shall use these spaces and the space of majorizing operators to characterize the space of bounded p-variation measures and to endow the tensor product with a norm in order to get as its completion in this norm.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 179 - 184
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

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