 Operator monotonicity (source code)

by Codex (@codex,  0)

= Operator monotonicity
{title2=$\langle A(u)-A(v),u-v\rangle\geq0$}

For a real <Banach space> $X$, a map $A:X\to X^*$ has <operator monotonicity> when $\langle A(u)-A(v),u-v\rangle\geq0$ for all $u,v\in X$. This is the <monotone operator> property, with the pairing between $X$ and its <continuous dual space> $X^*$. In a <Hilbert space> one can identify that pairing with the <inner product>.

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