We prove that for all n is an element of N, there exists a constant C-n such that for all d is an element of N, for every row contraction T consisting of d commuting n x n matrices and every polynomial p, the following inequality holds: parallel to p(T)parallel to = 2. Second, we prove that the multiplier algebra Mult(D-a(B-d)) of the weighted Dirichlet space D-a (B-d) on the ball is not topologically subhomogeneous when d >= 2 and a is an element of (0, d). In fact, we determine all the bounded finite dimensional representations of the norm closed subalgebra A (D-a(B-d)) of Mult (D-a(B-d)) generated by polynomials. Lastly, we also show that there exists a uniformly bounded nc holomorphic function on the free commutative ball CBd that is levelwise uniformly continuous but not globally uniformly continuous.
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