Let $H$ be a Hilbert space.
$$T:D \rightarrow H$$ be a densely defined unbounded operator. Suppose $\dim \ker T < \infty$. Let $\bar{T}$ be its closure, supposing its existence.
Is it true that $\dim \ker \bar{T}= \dim \ker T$?
2026-03-27 10:09:55.1774606195
Dimension of kernel of closure of an unbounded operator
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