On the joint spectral radius

ArticleOriginal scientific text

Title

Authors ¹

Mathematical Institute, Academy of Sciences of The Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

We prove the

_p

-spectral radius formula for n-tuples of commuting Banach algebra elements

Banach algebra, spectrum, spectral radius

M. A. Berger and Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21-27.
J. W. Bunce, Models for n-tuples of non-commuting operators, J. Funct. Anal. 57 (1984), 21-30.
M. Chō and T. Huruya, On the spectral radius, Proc. Roy. Irish Acad. Sect. A 91 (1991), 39-44.
M. Chō and W. Żelazko, On geometric spectral radius of commuting n-tuples of operators, Hokkaido Math. J. 21 (1992), 251-258.
C.-K. Fong and A. Sołtysiak, Existence of a multiplicative linear functional and joint spectra, Studia Math. 81 (1985), 213-220.
V. Müller and A. Sołtysiak, Spectral radius formula for commuting Hilbert space operators, Studia Math. 103 (1992), 329-333.
P. Rosenthal and A. Sołtysiak, Formulas for the joint spectral radius of non-commuting Banach algebra elements, Proc. Amer. Math. Soc. 123 (1995), 2705-2708.
G.-C. Rota and W. G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379-381.
A. Sołtysiak, On a certain class of subspectra, Comment. Math. Univ. Carolin. 32 (1991), 715-721.
A. Sołtysiak, On the joint spectral radii of commuting Banach algebra elements, Studia Math. 105 (1993), 93-99.