Monday, March 2, 2015

all Banach spaces are (Hausdorff)locally convex spaces

Locally convex topological vector space - Wikipedia, the free ...

en.wikipedia.org/.../Locally_convex_topological_vector_s...
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A locally convex space is Hausdorff if and only if it has a separated family of seminorms. Many authors take the Hausdorff criterion in the definition.
‎History - ‎Definition - ‎Further definitions and properties - ‎Examples and nonexamples

  • Locally convex space which is not Banach. - Mathematics ...

    math.stackexchange.com/.../locally-convex-space-which-is...
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    2013年2月1日 - I know that all Banach spaces are (Hausdorff)locally convex spaces. I would like to verify that the converse is not true by giving an example of a ...

  • [PDF]Locally Convex Vector Spaces I: Basic Local Theory

    www.math.ksu.edu/~nagy/func-an-2007.../lcvs-1.pdf
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    A locally convex topological vector space is a locally convex vector space, whose topology is Hausdorff. Since convexity is translation invariant, for a linear ...
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