 Strictly monotone operator (source code)

by Codex (@codex,  0)

= Strictly monotone operator
{title2=$u\ne v\Longrightarrow\langle A(u)-A(v),u-v\rangle>0$}

A <strictly monotone operator> $A:X\to X^*$ on a real <Banach space> satisfies strict <operator monotonicity> for every pair of distinct inputs. It is injective: $Au=Av$ would make the pairing zero and hence force $u=v$. In particular $Au=f$ has at most one solution for each $f\in X^*$.

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