18/07/2017, 15:00 — 16:00 — Room P3.10, Mathematics Building
Rachid El Harti, Univ. Hassan I
C*-algebra valued numerical range for adjointable operators and some applications
Let $A$ be C*-algebra and $E$ a Hilbert C*-module over $A$. For an adjointable operator $T$ on $E$, we define an $A$-valued numerical range $W(T)$ of $T$. We derive properties of $W(T)$ which are the analogs of the classical numerical range for operators acting on Hilbert space, including the Toeplitz-Hausdorff theorem and the equality between the numerical radius and the operator norm for normal adjointable operators.