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Topological vector space with a locally convex topology, i.e. induced by a system of seminorms.

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Does $End(V)$ remember $V$, where $V$ is a locally convex space?

If $V$ is a Mackey space (for example, a Banach space), $\text{End} (V)$ coincides with $\text{End} (V_\sigma)$, where $V_\sigma$ denotes $V$ with the weak topology.
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