The aim of this paper is to characterize a class of subspectra for which the geometric spectral radius is the same and depends only upon a commuting $n$-tuple of elements of a complex Banach algebra. We prove also that all these subspectra have the same capacity.
@article{118451, author = {Andrzej So\l tysiak}, title = {On a certain class of subspectra}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {715-721}, zbl = {0763.46037}, mrnumber = {1159818}, language = {en}, url = {http://dml.mathdoc.fr/item/118451} }
Sołtysiak, Andrzej. On a certain class of subspectra. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 715-721. http://gdmltest.u-ga.fr/item/118451/
Boundary points of joint numerical ranges, Pacific J. Math. 95 (1981), 27-35. (1981) | MR 0631656
On geometric spectral radius of commuting $n$-tuples of operators, to appear in Hokkaido Math. J. | MR 1169792
A note on semicharacters, in: Banach Center Publications, vol. 8, Spectral Theory, PWN, Warsaw, 1982, 397-402. | MR 0738305
Capacity of finite systems of elements in Banach algebras, Comment. Math. 19 (1977), 381-387. (1977) | MR 0477779
Some remarks on the joint capacities in Banach algebras, ibid. 20 (1978), 197-204. (1978) | MR 0463939
The joint capacity of elements of Banach algebras, J. London Math. Soc. (2), 10 (1975), 212-218. (1975) | MR 0370195 | Zbl 0302.46035
An axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261. (1979) | MR 0544729
Banach Algebras, Elsevier, PWN, Amsterdam, Warsaw, 1973. | MR 0448079