We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
@article{bwmeta1.element.bwnjournal-article-smv105i1p69bwm,
author = {Vladim\'\i r M\"uller},
title = {The S\l odkowski spectra and higher Shilov boundaries},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {69-75},
zbl = {0812.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p69bwm}
}
Müller, Vladimír. The Słodkowski spectra and higher Shilov boundaries. Studia Mathematica, Tome 104 (1993) pp. 69-75. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv105i1p69bwm/
[00000] [1] E. Albrecht and F.-H. Vasilescu, Stability of the index of a semi-Fredholm complex of Banach spaces, J. Funct. Anal. 66 (1986), 141-172. | Zbl 0592.47008
[00001] [2] R. Basener, A generalized Shilov boundary and analytic structure, Proc. Amer. Math. Soc. 47 (1975), 98-104. | Zbl 0296.46056
[00002] [3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. | Zbl 0271.46039
[00003] [4] J. J. Buoni, R. Harte and T. Wickstead, Upper and lower Fredholm spectra, Proc. Amer. Math. Soc. 66 (1977), 309-314. | Zbl 0375.47001
[00004] [5] M. Chō and M. Takaguchi, Boundary of Taylor's joint spectrum for two commuting operators, Sci. Rep. Hirosaki Univ. 28 (1981), 1-4. | Zbl 0499.47001
[00005] [6] G. Corach and F. D. Suárez, Generalized rational convexity in Banach algebras, Pacific J. Math. 140 (1989), 35-51. | Zbl 0705.46029
[00006] [7] R. E. Curto, Connections between Harte and Taylor spectrum, Rev. Roumaine Math. Pures Appl. 31 (1986), 203-215. | Zbl 0609.47007
[00007] [8] A. S. Faĭnshteĭn, Joint essential spectrum of a family of linear operators, Funct. Anal. Appl. 14 (1980), 152-153.
[00008] [9] A. S. Faĭnshteĭn, Stability of Fredholm complexes of Banach spaces with respect to perturbations which are small in q-norms, Izv. Akad. Nauk Azerbaǐdzhan. SSR Ser. Fiz.-Tekhn. Mat. Nauk 1980 (1), 3-8 (in Russian).
[00009] [10] K.-H. Förster and E.-O. Liebentrau, Semi-Fredholm operators and sequence conditions, Manuscripta Math. 44 (1983), 35-44. | Zbl 0519.47009
[00010] [11] M. Putinar, Functional calculus and the Gelfand transformation, Studia Math. 84 (1984), 83-86. | Zbl 0498.47009
[00011] [12] B. N. Sadovskiĭ, Limit-compact and condensing operators, Russian Math. Surveys 27 (1972), 85-155. | Zbl 0243.47033
[00012] [13] N. Sibony, Multidimensional analytic structure in the spectrum of a uniform algebra, in: Spaces of Analytic Functions, Kristiansand, Norway 1975, Lecture Notes in Math. 512, Springer, Berlin, 139-175.
[00013] [14] Z. Słodkowski, An infinite family of joint spectra, Studia Math. 61 (1977), 239-255. | Zbl 0369.47021
[00014] [15] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, ibid. 50 (1974), 127-148. | Zbl 0306.47014
[00015] [16] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. | Zbl 0233.47024
[00016] [17] J. L. Taylor, The analytic functional calculus for several commuting operators, Acta Math. 125 (1970), 1-38. | Zbl 0233.47025
[00017] [18] T. Tonev, New relations between Sibony-Basener boundaries, in: Complex Analysis III, C. A. Berenstein (ed.), Lecture Notes in Math. 1277, Springer, Berlin 1987, 256-262. | Zbl 0628.46056
[00018] [19] V. Wrobel, The boundary of Taylor's joint spectrum for two commuting Banach space operators, Studia Math. 84 (1986), 105-111. | Zbl 0619.47002