This is an announcement for the paper "On different definitions of numerical range" by Miguel Martin.
Abstract: We study the relation between the intrinsic and the spatial numerical ranges with the recently introduced ``approximated'' spatial numerical range. As main result, we show that the intrinsic numerical range always coincides with the convex hull of the approximated spatial numerical range. Besides, we show sufficient conditions and necessary conditions to assure that the approximated spatial numerical range coincides with the closure of the spatial numerical range.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A12, Secondary 46B20
Remarks: 9 pages
Submitted from: mmartins@ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1502.07079
or