Skip to main content

Timeline for Algebraic Dual / Continuous Dual

Current License: CC BY-SA 2.5

5 events
when toggle format what by license comment
Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Feb 4, 2010 at 8:30 comment added Yemon Choi FWIW not every Banach space has a Schauder basis. If memory serves rightly, the first counter-example was due to Per Enflo. That said, the gap between Schauder basis and Hamel basis is vast in infinite dimensions
Feb 4, 2010 at 3:36 comment added Jonas Meyer Oh, in case it is confusing, the examples Ady gave are now in the comment by Scott Morrison, $l^\infty(\mathbb{N})$ and $C[0,1]^*$.
Feb 4, 2010 at 3:20 comment added Jonas Meyer (1)What about the examples Ady gives in the comments above? (2)What in general do you mean by topological basis? For Hilbert space I assume you mean orthonormal basis, and more generally some Banach spaces have Schauder bases, but I don't know if an analogous set exists in every Banach space. (3) Your characterization of the topological dual isn't accurate; you can't send the "topological basis" just anywhere. E.g., consider the identification of the dual of $l^2$ with $l^2$. (This point, however, only shows that the topological dual is "smaller" than you indicated.)
Feb 4, 2010 at 1:52 history answered Ilya Grigoriev CC BY-SA 2.5