The index of a not necessarily bounded self-adjoint operator $D$ on a Hilbert space $\cal H$ is "well-known" to be zero. What is the easiest way to see this. Moreover, does this automatically imply that the dimensions of the kernel and cokernel of $D$ are finite, and does it imply closure of the cokernel?
2026-03-28 15:26:16.1774711576
Vanishing Index of an Unbounded Self-Adjoint Operator
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