Two-isometries on Pontryagin spaces (Q939143)

A 2-isometry on a Pontryagin space is a linear operator \(T\) satisfying the identity \(T^{*2}T^2--2T^*T+I=0\). The author gives a functional model for a class of cyclic analytic 2-isometries, generalizing a Hilbert space version given by \textit{S.\,Richter} [Trans.\ Am.\ Math.\ Soc.\ 328, No.\,1, 325--349 (1991; Zbl 0762.47009)]. In addition, an example is constructed showing that, in contrast to the Hilbert space case, a cyclic analytic 2-isometry need not have a cyclic vector in the orthogonal complement of its range.