Notes
A more precise definition is given below.
Here the square root of the self-adjoint operator A ∗ A is defined using functional calculus similarly to the way one defines the square root of a positive definite matrix.
This expression is borrowed from a letter by J. Dixmier to the conference “Singular Traces and Their Applications” Luminy 2012, a quote to be found in a note of the monograph.
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Paycha, S. Steven Lord, Fedor Sukochev, Dmitriy Zanin: “Singular Traces, Theory and Applications”. Jahresber. Dtsch. Math. Ver. 116, 129–134 (2014). https://doi.org/10.1365/s13291-014-0087-5
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DOI: https://doi.org/10.1365/s13291-014-0087-5