Axiomatic theory of spectrum III: semiregularities

Vladimír Müller

Studia Mathematica (2000)

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

Abstract

top
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

top

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

top
  1. [G] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337. Zbl0477.47013
  2. [GL] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17-32. Zbl0203.45601
  3. [H1] R. Harte, On the exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114-118. Zbl0338.46043
  4. [H2] R. Harte, Fredholm theory relative to a Banach algebra homomorphism, Math. Z. 179 (1982), 431-436. Zbl0479.47032
  5. [H3] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, 1988. Zbl0636.47001
  6. [K] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. Zbl0148.12601
  7. [KM] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), 109-128. Zbl0857.47001
  8. [KMR] V. Kordula, V. Müller and V. Rakočević, On the semi-Browder spectrum, Studia Math. 123 (1997), 1-13. Zbl0874.47007
  9. [MM] M. Mbekhta and V. Müller, On the axiomatic theory of spectrum II, ibid. 119 (1996), 129-147. Zbl0857.47002
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.