# Axiomatic theory of spectrum III: semiregularities

Studia Mathematica (2000)

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

## Access Full Article

top## Abstract

top## How to cite

topMüller, 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- [G] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337. Zbl0477.47013
- [GL] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17-32. Zbl0203.45601
- [H1] R. Harte, On the exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114-118. Zbl0338.46043
- [H2] R. Harte, Fredholm theory relative to a Banach algebra homomorphism, Math. Z. 179 (1982), 431-436. Zbl0479.47032
- [H3] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, 1988. Zbl0636.47001
- [K] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966. Zbl0148.12601
- [KM] V. Kordula and V. Müller, On the axiomatic theory of spectrum, Studia Math. 119 (1996), 109-128. Zbl0857.47001
- [KMR] V. Kordula, V. Müller and V. Rakočević, On the semi-Browder spectrum, Studia Math. 123 (1997), 1-13. Zbl0874.47007
- [MM] M. Mbekhta and V. Müller, On the axiomatic theory of spectrum II, ibid. 119 (1996), 129-147. Zbl0857.47002
- [MW] A. M. Meléndez and A. Wawrzyńczyk, An approach to joint spectra, Ann. Polon. Math. 72 (1999), 131-144. Zbl0967.46033
- [O1] K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212. Zbl0277.47002
- [O2] K. K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), 365-373. Zbl0439.47008
- [R1] V. Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193-198. Zbl0602.47003
- [R2] V. Rakočević, On the essential spectrum, Zb. Rad. 6 (1992), 39-48. Zbl0913.47005
- [S] M. Schechter, On the essential spectrum of an arbitrary operator, J. Math. Anal. Appl. 13 (1966), 205-215. Zbl0147.12101
- [Z1] J. Zemánek, Compressions and the Weyl-Browder spectra, Proc. Roy. Irish Acad. Sect. A 86 (1986), 57-62. Zbl0617.47001
- [Z2] J. Zemánek, Approximation of the Weyl spectrum, ibid. 87 (1987), 177-180. Zbl0647.47001

## Citations in EuDML Documents

top## NotesEmbed ?

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