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An unpleasant set in a non-locally-convex vector lattice
Published online by Cambridge University Press: 20 January 2009
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In a linear topological space E one often carries out various “ smoothing ” operations on a subset A, such as taking the convex hull co A and the closure A-. If E is also a (real) vector lattice, the solid hull
is also a natural “ smoothing out ” of A. If sol A = A then A is called solid, and if E has a base of solid neighbourhoods of 0 as do all the common topological vector lattices such as C(X), Lp, Köthe spaces and so on—then E is called a locally solid space.
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- Copyright © Edinburgh Mathematical Society 1973
References
REFERENCES
(1) Chacon, R. V. and Krengel, U., Linear modulus of a linear operator, Proc. Amer. Math. Soc. 15 (1964), 553–559.Google Scholar
(4) Feller, W., Introduction to Probability Theory and Applications, Vol. 2 (Wiley, 1966).Google Scholar
(5) Kingman, J. F. C. and Taylor, S. J., Introduction to Measure and Probability (Cambridge, 1966).Google Scholar
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