Models for q-commutative tuples of isometries

2022/07/04 by Ball, Joseph A., Sau, Haripada · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2207.01278

Abstract

A pair of Hilbert space linear operators (V₁,V₂) is said to be q-commutative, for a unimodular complex number q, if V₁V₂=qV₂V₁. A concrete functional model for q-commutative pairs of isometries is obtained. The functional model is parametrized by a collection of Hilbert spaces and operators acting on them. As a consequence, the collection serves as a complete unitary invariance for q-commutative pairs of isometries. A q-commutative operator pair (V₁,V₂) is said to be doubly q-commutative, if in addition, it satisfies V₂V₁^*=qV₁^*V₂. Doubly q-commutative pairs of isometries are also characterized. Special attention is given to doubly q-commutative pairs of shift operators. The notion of q-commutativity is then naturally extended to the case of general tuples of operators to obtain a similar model for tuples of q-commutative isometries.

Cited by

• The q-commuting contractions and *-regular dilations

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