Abstract
Given a convex domain C with conic boundary, a linear operator A with numerical range contained in , and a rational function bounded on , we are interested in estimating the norm of r(A) in terms of the supremum of r in . In particular, we show that ellipses, hyperbolas and parabolas are K-spectral sets with K = 2 + 2= p 3 3:16. 2000 Mathematical subject classications : 47A12 ; 47A25
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