MATHEMATICA BOHEMICA, Vol. 124, No. 2–3, pp. 185-192 (1999)

Alcune osservazioni sul rango numerico per operatori non lineari

J. Appell, G. Conti, P. Santucci

Jürgen Appell, Universität Würzburg, Mathematisches Institut, Am Hubland, D-97074 Würzburg, Germany, e-mail: appell@mathematik.uni-wuerzburg.de; Giuseppe Conti, Universita di Firenze, Istituto di Matematica, Via dell'Agnolo 14, I-50122 Firenze, Italy, e-mail: gconti@cesit1.unifi.it; Paola Santucci, Universita di Roma "La Sapienza", Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Via A. Scarpa 16, I-00161 Roma, Italy, e-mail: bigi@dmmm.uniroma1.it

Abstract: We discuss some numerical ranges for Lipschitz continuous nonlinear operators and their relations to spectral sets. In particular, we show that the spectrum defined by Kachurovskij (1969) for Lipschitz continuous operators is contained in the so-called polynomial hull of the numerical range introduced by Rhodius (1984).

Keywords: nonlinear operator, Lipschitz continuity, spectrum, numerical range, convex hull, polynomial hull

Classification (MSC2000): 47A12, 47H09, 47H12, 47H17, 65F99, 15A60

Full text of the article:

Compressed PostScript file (124 kilobytes)
PDF file (120 kilobytes)

[Previous Article] [Next Article] [Contents of this Number]