Balanced doubly contractive weighted shifts admit spherical unitary dilations and satisfy the ball version of von Neumann inequality; general commuting doubly contractive tuples satisfy it for homogeneous polynomials of degree ≤2.
Shields, Weighted shift operators and analytic function theory, inTopics in Operator Theory, Math
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von Neumann Inequality for a class of Doubly Contractive Weighted Shifts
Balanced doubly contractive weighted shifts admit spherical unitary dilations and satisfy the ball version of von Neumann inequality; general commuting doubly contractive tuples satisfy it for homogeneous polynomials of degree ≤2.