Thenumber of points where a linear mapping from into attains its norm

Abstract

Let S be a regular -matrix mapping onto , , with norm (Error rendering LaTeX formula) . Then we are interested in the set (Error rendering LaTeX formula) i.e. the set of points on the unit sphere where S attains its norm. We prove for .This follows from properties of the Taylor expansion of near points in C. The case remains open. But we show by an example that for the behaviour of may be completely different as for .