We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-3, author = {Mohammad Ali Ardalani}, title = {Numerical index with respect to an operator}, journal = {Studia Mathematica}, volume = {223}, year = {2014}, pages = {165-171}, zbl = {1316.47006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-3} }
Mohammad Ali Ardalani. Numerical index with respect to an operator. Studia Mathematica, Tome 223 (2014) pp. 165-171. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-3/