Cyclically monotone linear operators
Elias S. W. Shiu · Proceedings of the American Mathematical Society · 1976
A linear operator on a complex Hilbert space H \mathcal {H} is called n n -cyclically monotone if for each sequence x 0 , x 1 , … , x n − 1 , x n = x 0 {x_0},{x_1}, \ldots ,{x_{n - 1}},{x_n} = {x_0} of n n elements in H , Σ j = 0 n − 1 Re ( T x j − x j + 1 ) ⩾ 0 \mathcal {H},\Sigma _{j = 0}^{n - 1}\operatorname {Re} (T{x_j} - {x_{j + 1}}) \geqslant 0 . We show that T T is n n -cyclically monotone if and only if | Arg ( T x , x )