The Słodkowski spectra and higher Shilov boundaries

Vladimír Müller

Studia Mathematica (1993)

  • Volume: 105, Issue: 1, page 69-75
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Müller, Vladimír. "The Słodkowski spectra and higher Shilov boundaries." Studia Mathematica 105.1 (1993): 69-75. <http://eudml.org/doc/215984>.

@article{Müller1993,
abstract = {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.},
author = {Müller, Vladimír},
journal = {Studia Mathematica},
keywords = {higher Shilov boundaries of the Taylor spectrum; approximate point spectrum},
language = {eng},
number = {1},
pages = {69-75},
title = {The Słodkowski spectra and higher Shilov boundaries},
url = {http://eudml.org/doc/215984},
volume = {105},
year = {1993},
}

TY - JOUR
AU - Müller, Vladimír
TI - The Słodkowski spectra and higher Shilov boundaries
JO - Studia Mathematica
PY - 1993
VL - 105
IS - 1
SP - 69
EP - 75
AB - 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.
LA - eng
KW - higher Shilov boundaries of the Taylor spectrum; approximate point spectrum
UR - http://eudml.org/doc/215984
ER -

References

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  2. [2] R. Basener, A generalized Shilov boundary and analytic structure, Proc. Amer. Math. Soc. 47 (1975), 98-104. Zbl0296.46056
  3. [3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973. Zbl0271.46039
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  5. [5] M. Chō and M. Takaguchi, Boundary of Taylor's joint spectrum for two commuting operators, Sci. Rep. Hirosaki Univ. 28 (1981), 1-4. Zbl0499.47001
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  14. [14] Z. Słodkowski, An infinite family of joint spectra, Studia Math. 61 (1977), 239-255. Zbl0369.47021
  15. [15] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, ibid. 50 (1974), 127-148. Zbl0306.47014
  16. [16] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. Zbl0233.47024
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  19. [19] V. Wrobel, The boundary of Taylor's joint spectrum for two commuting Banach space operators, Studia Math. 84 (1986), 105-111. Zbl0619.47002

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