Five classes of monotone linear relations and operators

The relationships between five classes of monotonicity, namely 3^*-, 3-cyclic, strictly, para-, and maximal monotonicity, are explored for linear operators and linear relations in Hilbert space. Where classes overlap, examples are given; otherwise their relationships are noted for linear operators in ${\mathcal{R}}^2$, ${\mathcal{R}}^n$, and general Hilbert spaces. Along the way, some results for linear relations are obtained.