locally convex topological vector space
Definition Let $V$ be a topological vector space^{} over a subfield^{} of the complex numbers^{} (usually taken to be $\mathbb{R}$ or $\u2102$). If the topology of $V$ has a basis where each member is a convex set, then $V$ is a locally convex topological vector space [1].
Though most vector spaces occurring in practice are locally convex, the spaces ${L}^{p}$ for $$ are examples of spaces which are not locally convex.
References
- 1 G.B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd ed, John Wiley & Sons, Inc., 1999.
Title | locally convex topological vector space |
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Canonical name | LocallyConvexTopologicalVectorSpace |
Date of creation | 2013-03-22 13:44:03 |
Last modified on | 2013-03-22 13:44:03 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 9 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 46A03 |
Classification | msc 46-00 |