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Question: the test function space is reflexive ?

and the adherence of this space is it again reflexive ?

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closed as off-topic by user44191, abx, Sean Lawton, Wolfgang, Jan-Christoph Schlage-Puchta May 12 at 15:55

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    $\begingroup$ You should specify what you mean by the space of test functions. If you mean the usual space ${\mathcal D}(U)$, then it is reflexive as a Montel space (this is written explicitely in R.Edwards' Functional analysis, 8.4.7). It is also not clear what you mean by adherence. And I think you should ask this at math.stackexchange.com $\endgroup$ – Sergei Akbarov May 11 at 15:30