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 α=(α1,…,αs) of natural numbers. A pure algebraic isopair of finite bimultiplicity with rank α, acting on a Hilbert space, is nearly max-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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