On Euclidean algebra of hermitian operators on a quadratic Hilbert spaceStrašek, Rok (Avtor) mathematicsEuclidean algebrasquaternionic Hilbert spaceultraprime algebrasJacobson-McCrimmon operatorspectral normWe solve the problem of finding the best possible constant of ultraprimeness for the special class of Euclidean algebra called algebra of hermitian operators on a quaternionic Hilbert space. More precisely, we prove that for algebra of hermitian operators, equipped with spectral norm, the best possibleconstant of ultraprimeness is 1/2.20062012-05-30 14:40:38Neznano25674sl