An approach to joint spectra

Angel Martínez Meléndez; Antoni Wawrzyńczyk

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 2, page 131-144
  • ISSN: 0066-2216

Abstract

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For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.

How to cite

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Martínez Meléndez, Angel, and Wawrzyńczyk, Antoni. "An approach to joint spectra." Annales Polonici Mathematici 72.2 (1999): 131-144. <http://eudml.org/doc/262705>.

@article{MartínezMeléndez1999,
abstract = {For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.},
author = {Martínez Meléndez, Angel, Wawrzyńczyk, Antoni},
journal = {Annales Polonici Mathematici},
keywords = {spectral subspace; joint spectrum; Banach algebra; Banach algebras; spectral subspaces; spectral systems; spectral mapping property},
language = {eng},
number = {2},
pages = {131-144},
title = {An approach to joint spectra},
url = {http://eudml.org/doc/262705},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Martínez Meléndez, Angel
AU - Wawrzyńczyk, Antoni
TI - An approach to joint spectra
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 2
SP - 131
EP - 144
AB - For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.
LA - eng
KW - spectral subspace; joint spectrum; Banach algebra; Banach algebras; spectral subspaces; spectral systems; spectral mapping property
UR - http://eudml.org/doc/262705
ER -

References

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  1. [1] C.-K. Fong and A. Sołtysiak, Existence of a multiplicative functional and joint spectra, Studia Math. 81 (1985), 213-220. Zbl0529.46034
  2. [2] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, 1988. Zbl0636.47001
  3. [3] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), 109-128. Zbl0857.47001
  4. [4] V. Müller, Spectral systems, unpublished notes, 1997. 
  5. [5] A. Sołtysiak, Approximate point joint spectrum and multiplicative functionals, Studia Math. 86 (1987), 227-286. Zbl0646.46041
  6. [6] A. Sołtysiak, Joint spectra and multiplicative functionals, Colloq. Math. 56 (1989), 357-366. 
  7. [7] A. Sołtysiak, Joint Spectra and Multiplicative Linear Functionals in Non-commutative Banach Algebras, Wyd. Nauk. Uniw. im. A. Mickiewicza, Poznań, 1988. Zbl0675.46018
  8. [8] W. Żelazko, An axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261. Zbl0426.47002

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