Nearly exotic topologies on normed spaces |
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Authors: | N T Peck |
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Institution: | (1) University of Illinois, Urbana, Illinois |
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Abstract: | It is proved that for every infinite dimensional normed space (E, ‖ ‖) there is a non-trivial linear space topologyτ onE which is weaker than the norm topology and is such that (E, τ) admits no non-trivial continuous linear functionals. IfE is a space with a generalized basis or is aC(X) space, it is proved that the topologyτ can be taken to be Hausdorff. |
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