Normal essential eigenvalues in the boundary of the numerical range
Norberto Salinas, Maria Velasco · Proceedings of the American Mathematical Society · 2000
A purely geometric property of a point in the boundary of the numerical range of an operator T T on Hilbert space is examined which implies that such a point is the value at T T of a multiplicative linear functional of the C ∗ C^* -algebra, C ∗ ( T ) C^*(T) , generated by T T and the identity operator. Roughly speaking, such a property means that the boundary of the numerical range (of T T ) has infinite curvature at that point. Furthermore, it is shown that if such a point is not a sharp linear corner of the numerical range of T T , then the multiplicative linear functional vanishes on the compact operators in C ∗ ( T ) C^*(T) .