Geodesic
The boundary of the numerical range
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 69-72

Voir la notice de l'article provenant de la source Cambridge University Press

In [1] it was shown that for a compact normal operator on a Hilbert space the numerical range was the convex hull of the point spectrum. Here it is shown that the same holds for a semi-normal operator whose point spectrum satisfies a density condition (Theorem 1). In Theorem 2 a similar condition is shown to imply that the numerical range of a semi-normal operator is closed. Some examples are given to indicate that the condition in Theorem 1 cannot be relaxed too much. 
Barra, G. de. The boundary of the numerical range. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 69-72. doi: 10.1017/S001708950000447X
@article{10_1017_S001708950000447X,
     author = {Barra, G. de},
     title = {The boundary of the numerical range},
     journal = {Glasgow mathematical journal},
     pages = {69--72},
     year = {1981},
     volume = {22},
     number = {1},
     doi = {10.1017/S001708950000447X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000447X/}
}
TY  - JOUR
AU  - Barra, G. de
TI  - The boundary of the numerical range
JO  - Glasgow mathematical journal
PY  - 1981
SP  - 69
EP  - 72
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000447X/
DO  - 10.1017/S001708950000447X
ID  - 10_1017_S001708950000447X
ER  - 
%0 Journal Article
%A Barra, G. de
%T The boundary of the numerical range
%J Glasgow mathematical journal
%D 1981
%P 69-72
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950000447X/
%R 10.1017/S001708950000447X
%F 10_1017_S001708950000447X

[1] 1.de Barra, G., Giles, J. R. and Sims, B., On the numerical range of operators, J. London Math. Soc. (2) 5 (1972), 704–706. Google Scholar | DOI

[2] 2.Embry, M. R., The numerical range of an operator, Pacific J. Math. 32 (1970), 647–650. Google Scholar | DOI

[3] 3.Embry, M. R., Orthogonality and the numerical range, J. Math. Soc. Japan 27 (3) (1975), 405–411. Google Scholar | DOI

[4] 4.MacCluer, C. R., On extreme points of the numerical range of normal operators, Proc. Amer. Math. Soc. 16 (1965), 1183–1184. Google Scholar | DOI

[5] 5.Meng, Ching-Hwa, A condition that a normal operator have a closed numerical range, Proc. Amer. Math. Soc. 8 (1957), 85–88. Google Scholar | DOI

[6] 6.Putnam, C. R., On the spectra of semi-normal operators, Trans. Amer. Math. Soc. 119 (1965), 509–523. Google Scholar | DOI

[7] 7.Stampfli, J. G., Hyponormal operators, Pacific J. Math. 12 (1962), 1453–1458. Google Scholar | DOI

[8] 8.Stampfli, J. G., Hyponormal operators and spectral density, Trans. Amer. Math. Soc. 117 (1965), 469–476. Google Scholar | DOI

[9] 9.Stampfli, J. G., Extreme points of the numerical range of a hyponormal operator, Michigan Math. J. 13 (1966). 87–89. Google Scholar | DOI

Cité par Sources :