On a certain class of subspectra

Andrzej Sołtysiak

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 715-721
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Sołtysiak, Andrzej. "On a certain class of subspectra." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 715-721. <http://eudml.org/doc/247300>.

@article{Sołtysiak1991,
abstract = {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.},
author = {Sołtysiak, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Banach algebra; joint spectrum; subspectrum; spectroid; geometrical spectral radius; (joint) capacity; joint spectrum; spectroid; subspectra; geometric spectral radius; capacity},
language = {eng},
number = {4},
pages = {715-721},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a certain class of subspectra},
url = {http://eudml.org/doc/247300},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Sołtysiak, Andrzej
TI - On a certain class of subspectra
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 715
EP - 721
AB - 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.
LA - eng
KW - Banach algebra; joint spectrum; subspectrum; spectroid; geometrical spectral radius; (joint) capacity; joint spectrum; spectroid; subspectra; geometric spectral radius; capacity
UR - http://eudml.org/doc/247300
ER -

References

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  1. Chō M., Takaguchi M., Boundary points of joint numerical ranges, Pacific J. Math. 95 (1981), 27-35. (1981) MR0631656
  2. Chō M., Żelazko W., On geometric spectral radius of commuting n -tuples of operators, to appear in Hokkaido Math. J. MR1169792
  3. Słodkowski Z., Żelazko W., A note on semicharacters, in: Banach Center Publications, vol. 8, Spectral Theory, PWN, Warsaw, 1982, 397-402. MR0738305
  4. Sołtysiak A., Capacity of finite systems of elements in Banach algebras, Comment. Math. 19 (1977), 381-387. (1977) MR0477779
  5. Sołtysiak A., Some remarks on the joint capacities in Banach algebras, ibid. 20 (1978), 197-204. (1978) MR0463939
  6. Stirling D.S.G., The joint capacity of elements of Banach algebras, J. London Math. Soc. (2), 10 (1975), 212-218. (1975) Zbl0302.46035MR0370195
  7. Żelazko W., An axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261. (1979) MR0544729
  8. Żelazko W., Banach Algebras, Elsevier, PWN, Amsterdam, Warsaw, 1973. MR0448079

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