caa a22 4500 388046635 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199810 xx s 000 0 eng 10.1017/S1446788700034996 doi S1446788700034996 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700034996 On the numerical range map [Elektronische Daten] Let A (Cn) and A1, A2 be the unique Hermitian operators such that A = A1 + i A2. The paper is concerned with the differential structure of the numerical range map nA: x ((A1x, x), (A1x, x)) and its connection with certain natural subsets of the numerical range W(A) of A. We completely characterize the various sets of critical and regular points of the map nA as well as their respective images within W(A). In particular, we show that the plane algebraic curves introduced by R. Kippenhahn appear naturally in this context. They basically coincide with the image of the critical points of nA. Copyright © Australian Mathematical Society 1998 15A22 nationallicence 15A60 nationallicence Joswig M. Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany Straub B. School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 267-283 1446-7887 65:2<267 1998 65 JAZ https://doi.org/10.1017/S1446788700034996 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700034996 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Joswig M. Fachbereich Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany NATIONALLICENCE 700 1- Straub B. School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/2(1998-10), 267-283 1446-7887 65:2<267 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge