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Axiomatic theory of spectrum III: semiregularities

Vladimír Müller

Studia Mathematica (2000)

  • Volume: 142, Issue: 2, page 159-169
  • ISSN: 0039-3223

Abstract

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We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).

How to cite

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Müller, Vladimír. "Axiomatic theory of spectrum III: semiregularities." Studia Mathematica 142.2 (2000): 159-169. <http://eudml.org/doc/216795>.

@article{Müller2000,
abstract = {We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).},
author = {Müller, Vladimír},
journal = {Studia Mathematica},
keywords = {spectral mapping; essential spectrum; upper and lowr semiregularities; spectral mapping theorems},
language = {eng},
number = {2},
pages = {159-169},
title = {Axiomatic theory of spectrum III: semiregularities},
url = {http://eudml.org/doc/216795},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Müller, Vladimír
TI - Axiomatic theory of spectrum III: semiregularities
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 2
SP - 159
EP - 169
AB - We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).
LA - eng
KW - spectral mapping; essential spectrum; upper and lowr semiregularities; spectral mapping theorems
UR - http://eudml.org/doc/216795
ER -

References

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  10. [MW] A. M. Meléndez and A. Wawrzyńczyk, An approach to joint spectra, Ann. Polon. Math. 72 (1999), 131-144. Zbl0967.46033
  11. [O1] K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212. Zbl0277.47002
  12. [O2] K. K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), 365-373. Zbl0439.47008
  13. [R1] V. Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193-198. Zbl0602.47003
  14. [R2] V. Rakočević, On the essential spectrum, Zb. Rad. 6 (1992), 39-48. Zbl0913.47005
  15. [S] M. Schechter, On the essential spectrum of an arbitrary operator, J. Math. Anal. Appl. 13 (1966), 205-215. Zbl0147.12101
  16. [Z1] J. Zemánek, Compressions and the Weyl-Browder spectra, Proc. Roy. Irish Acad. Sect. A 86 (1986), 57-62. Zbl0617.47001
  17. [Z2] J. Zemánek, Approximation of the Weyl spectrum, ibid. 87 (1987), 177-180. Zbl0647.47001

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