Interpenetration of ellipsoids and the polynomial bound of a matrix Original Research Article

Long-standing problems in operator theory hinge on the manner in which the polynomial bound K(T) of a matrix T can differ from its completely (polynomially) bounded norm M(T). We introduce a new and simpler class of examples where K(T) < M(T) can occur. In particular, we show that this happens for certain 4 × 4 matrices, and that this phenomenon depends on the interpenetration of dual ellipsoids inscribed in a tetrahedron.