Strictly positive compact operator commuting with a given Fredholm operator

45 Views Asked by At

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?

enter image description here