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Convexity conditions for non-locally convex lattices

Published online by Cambridge University Press:  18 May 2009

N. J. Kalton
N. J. Kalton
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
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First we recall that a (real) quasi-Banach space X is a complete metrizable real vector space whose topology is given by a quasi-norm satisfying

where C is some constant independent of x1 and x2. X is said to be p-normable (or topologically p-convex), where 0 < p ≤ l, if for some constant B we have

for any x1, …, xn, є X. A theorem of Aolci and Rolewicz (see [18]) asserts that if in C = 21/p-1, then X is p-normable. We can then equivalently re-norm X so that in (1.4) B = 1.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 141 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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