Normal parts of certain operators
Normal parts of certain operators
Only bounded operators $T$ on a Hilbert space $\mathfrak{H}$ will be considered.A compact set $X$ of complex numbers containing $sp(T)$ is said to be a spectraI set of $T$ (von Neumann [8]) if $\Vert f(T)\Vert\leqq\sup_{z\in X}|f(z)|$ , where $f(z)$ is a rational function having no poles on $X$ ; cf.Riesz …