A Reverse Theorem on the ·-w* Continuity of the Dual Map
Given a Banach space X, x∈𝖲X, and 𝖩Xx=x*∈𝖲X*:x*x=1, we define the set 𝖩X*x of all x*∈𝖲X* for which there exist two sequences xnn∈N⊆𝖲X∖{x} and xn*n∈N⊆𝖲X* such that xnn∈N converges to x, xn*n∈N has a subnet w*-convergent to x*, and xn*xn=1 for all n∈N. We prove that if X is separable and reflexive and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/864173 |
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