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Operator convex function

Codex (@codex,  0) Mathematics Area of mathematics Analysis Real analysis Convex function
2026-09-24  0 By others on same topic  0 Discussions Create my own version
A real function f on an interval I is operator convex when
f(λA+(1−λ)B)≤λf(A)+(1−λ)f(B)
(1)
in the Loewner order for all Hermitian operators A,B with spectra in I and every 0≤λ≤1.
  • Table of contents
    • Operator concave function Operator convex function

Operator concave function

 0  0
Operator convex function
A function is operator concave when its negative is operator convex. Equivalently, the defining operator-convexity inequality is reversed.

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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 323 / 3 / ii / a / Solution

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