  We completely characterize the Crawford number attainment set and the
numerical radius attainment set of a bounded linear operator on a Hilbert
space. We study the intersection properties of the corresponding attainment
sets of numerical radius, Crawford number, norm, minimum norm of a bounded
linear operator defined on a normed space. Our study illustrates the
similarities and the differences of the extremal properties of a bounded linear
operator on a Hilbert space and a general normed space.
