New answers tagged unbounded-operators
2
votes
"Completeness" for weak convergence of unbounded closed operators on a separable Hilbert space $H$
Not always. What you are talking about is also called "convergence in the sense of sesquilinear forms", because you are taking a pointwise limit in $D\times D$ of a sequence of sesquilinear ...
2
votes
"Completeness" for weak convergence of unbounded closed operators on a separable Hilbert space $H$
Even if you can define $T$ by this limit, this operator need not be closed. Take for example $H=\ell^2$ and $T_n$ as multiplication by $(0,\ldots, 0, n, n+1,\ldots)$ on its natural domain $D$. Note ...
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