Journal of Operator Theory

Volume 79, Issue 2, Spring 2018 pp. 507-527.

Algebraic pairs of pure commuting isometries with finite multiplicity

Authors: Udeni D. Wijesooriya

Summary: An algebraic isopair is a commuting pair of pure isometries that is annihilated by a polynomial. The notion of the rank of a pure algebraic isopair with finite bimultiplicity is introduced as an $s$-tuple $\alpha=(\alpha_1,\ldots,\alpha_s)$ of natural numbers. A pure algebraic isopair of finite bimultiplicity with rank $\alpha$, acting on a Hilbert space, is nearly $\max\{\alpha_1,\ldots,\alpha_s\}$-cyclic and there is a finite codimensional invariant subspace such that the restriction to that subspace is $\max\{\alpha_1,\ldots,\alpha_s\}$-cyclic.

DOI: http://dx.doi.org/10.7900/jot.2017may12.2171
Keywords: commuting isometries, algebraic isopairs, cyclic operators, rational inner functions, distinguished varieties

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