Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.
@article{bwmeta1.element.bwnjournal-article-smv105i1p93bwm, author = {Andrzej So\l tysiak}, title = {On the joint spectral radii of commuting Banach algebra elements}, journal = {Studia Mathematica}, volume = {104}, year = {1993}, pages = {93-99}, zbl = {0811.46047}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p93bwm} }
Sołtysiak, Andrzej. On the joint spectral radii of commuting Banach algebra elements. Studia Mathematica, Tome 104 (1993) pp. 93-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p93bwm/
[00000] [1] M. A. Berger and Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21-27. | Zbl 0818.15006
[00001] [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. | Zbl 0271.46039
[00002] [3] M. Chō and W. Żelazko, On geometric spectral radius of commuting n-tuples of operators, Hokkaido Math. J. 21 (1992), 251-258. | Zbl 0784.47004
[00003] [4] R. E. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89-107. | Zbl 0206.13301
[00004] [5] A. Ya. Khelemskiĭ, Banach and Polynormed Algebras: General Theory, Representations, Homology, Nauka, Moscow 1989 (in Russian). | Zbl 0688.46025
[00005] [6] V. Müller and A. Sołtysiak, Spectral radius formula for commuting Hilbert space operators, Studia Math. 103 (1992), 329-333. | Zbl 0812.47004
[00006] [7] G.-C. Rota and W. G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379-381. | Zbl 0095.09701
[00007] [8] A. Sołtysiak, On a certain class of subspectra, Comment. Math. Univ. Carolinae 32 (1991), 715-721. | Zbl 0763.46037