Speaker
Edward Poon
Description
The spatial numerical range of an operator $T$ on a normed space $(\mathcal{X}, \| \cdot \|)$ is the set $$W(T) = \{f(Tx) : x \in \mathcal{X}, f \in \mathcal{X}^*, \|x\| = \|f\|^d = f(x) = 1\};$$ when $| \cdot |$ is induced by an inner product this coincides with the classical numerical range. We investigate some properties of the spatial numerical range.