I have shown that for a densely defined, self adjoint Operator D between Hilbert Spaces H, it holds $\inf \sigma(D)\geq c$ Is this enough to conclude, that $D$ is bounded below by c, i.e. $ < x, Dx> \geq c <x,x>$ for all $x \in Dom(D)$? Edit: if so, can you provide me a proof?
2026-02-22 21:15:29.1771794929
bounded below operator/ Kato-Rellich
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