In the following snippet from a paper by Jody Trout on the converse functional calculus, they mention the existence of a strictly positive compact operator $T$ commuting with a given self-adjoint, odd Fredholm operator on the standard graded Hilbert $A$-module. Could someone justify why such an operator always exists?
2026-03-25 18:45:44.1774464344
Strictly positive compact operator commuting with a given Fredholm operator
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