feat(CStarAlgebra): for a monotone f
on ℝ≥0
, ‖cfc f a‖ = f ‖a‖
#20819
+108
−4
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This PR shows various versions of the fact that if
f : ℝ≥0 → ℝ≥0
is monotone on the spectrum ofa
, then‖cfc f a‖ = f ‖a‖
. We then apply this result tosqrt
andrpow
.We also rename the file
Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow
toAnalysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic
, in order to put the new results in a new file with heavier imports. I think the new folder makes sense, especially since we'll need to do something like that anyway soon for the operator monotonicity and convexity/concavity results that depend on integral representations.