The three space problem for locally bounded F-spaces
نویسنده
چکیده
Let X be an F-space, and let Y be a subspace of X of dimension one, with X/Y = lp (0 p oo). Provided p ~ 1, X ~lp; however if p = 1, we construct an example to show that X need not be locally convex. More generally we show that Y is any closed subspace of X, then if Y is an r-Banach space (0 r:5 1) and XI Y is a p-Banach space with p r S 1 then X is a p-Banach space; if Y and XI Y are B-convex Banach spaces, then X is a B-convex Banach space. We give conditions on Y and XI Y which imply that Y is complemented in X. We also show that if X is the containing Banach space of a non-locally convex p-Banach space (p 1) with separating dual, then X is not B-convex. COMPOSITIO MATHEMATICA, Vol. 37, Fasc. 3, 1978, pag. 243-276. Sijthoff & Noordhoff International Publishers Alphen aan den Rijn Printed in the Netherlands
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