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Any analytic self-map of the open unit disk induces a bounded composition operator on the Hardy space H 2 and on the standard weighted Bergman spaces A 2 α. For a particular self-map, it is reasonable to wonder whether there is any meaningful relationship between the norms of the corresponding operators acting on each of these spaces. In this paper, we(More)
A non-negative pluriharmonic polynomial p(z) on the unit ball of C n is used as a weight against the rotationally invariant measure on the unit sphere. The resulting Hardy space carries the canonical n-tuple S of multiplication by the coordinate functions. By means of compressions of S to co-analytically invariant subspaces, and known estimates of the(More)
A subset S of the complex plane has n-fold symmetry about the origin (n-sato) if z ∈ S implies e 2π n z ∈ S. The 3 × 3 matrices A for which the numerical range W (A) has 3-sato have been characterized in two ways. First, W (A) has 3-sato if and only if the spectrum of A has 3-sato while tr(A 2 A *) = 0. In addition, W (A) has 3-sato if and only if A is(More)
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