Projections of Banach spaces
Copyright policy )Projections of Banach spaces
For we take X=m, E=co in the Lemma. REMARKS. 1. The method of [4] is to find a hereditary property of m which m/cO does not have. We found a nonhereditrary property preserved under projection. 2. An easy extension is available. All we used about the projection is that it is bounded and has a bounded right inverse Q. (Use Q' instead of u-*u|E in the proof.) Hence we see that there is no bounded map of m onto c0 which has a right inverse. 3. If E is isomorphic to a dual space there is always a bounded projection of E" onto E. Thus the Lemma yields the known fact that c0 is not isomorphic to a dual space. (Take X=co=M.) 4. Remark 3 also shows that if E (n has WS so does E(n-2) for all n>2.
- University of Reading United Kingdom
- Lehigh University United States
Normed linear spaces and Banach spaces; Banach lattices, General theory of locally convex spaces, Duality and reflexivity in normed linear and Banach spaces, Duality theory for topological vector spaces, Dilations, extensions, compressions of linear operators, Sequence spaces (including Köthe sequence spaces)
Normed linear spaces and Banach spaces; Banach lattices, General theory of locally convex spaces, Duality and reflexivity in normed linear and Banach spaces, Duality theory for topological vector spaces, Dilations, extensions, compressions of linear operators, Sequence spaces (including Köthe sequence spaces)
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