TY  - JOUR
AU  - Abdollahi, A. 
AU  - Heydari, M. T. 
AU  - Moosavi, M. 
PY  - 2009
TI  - On Numerical Ranges of Nilpotent Elements of C*-Algebra
JF  - Journal of Mathematics and Statistics
VL  - 5
IS  - 4
DO  - 10.3844/jmssp.2009.348.351
UR  - https://thescipub.com/jmss/jmssp.2009.348.351
AB  - Problem statement: Let A be a C*-algebra with unit 1. For each a∈A, let V(a), v(a) v0(a) and denote its numerical range, numerical radius and the distance from the origin to the boundary of its numerical range, respectively. Approach: If a is a nilpotent element of A with the power of nilpotency n, i.e., an = 0 and v(a) = (n-1) v0(a). Results: We proved that V(a) = bW(An), where b is a scalar and An is the strictly upper triangular n-by-n matrix with all entries above the main diagonal equal to one. Conclusion/Recommendations: We also completely determined the numerical range of such elements, by determining the numerical range of W(An) and showed that the boundary of it does not contain any arc of circle.
ER  -