# On the axiomatic theory of spectrum

Studia Mathematica (1996)

- Volume: 119, Issue: 2, page 109-128
- ISSN: 0039-3223

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topKordula, V., and Müller, V.. "On the axiomatic theory of spectrum." Studia Mathematica 119.2 (1996): 109-128. <http://eudml.org/doc/216289>.

@article{Kordula1996,

abstract = {There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).},

author = {Kordula, V., Müller, V.},

journal = {Studia Mathematica},

keywords = {axiomatic theory of spectrum; local spectrum; semiregular operators; Browder spectrum; Apostol spectrum},

language = {eng},

number = {2},

pages = {109-128},

title = {On the axiomatic theory of spectrum},

url = {http://eudml.org/doc/216289},

volume = {119},

year = {1996},

}

TY - JOUR

AU - Kordula, V.

AU - Müller, V.

TI - On the axiomatic theory of spectrum

JO - Studia Mathematica

PY - 1996

VL - 119

IS - 2

SP - 109

EP - 128

AB - There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).

LA - eng

KW - axiomatic theory of spectrum; local spectrum; semiregular operators; Browder spectrum; Apostol spectrum

UR - http://eudml.org/doc/216289

ER -

## References

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- [8] V. Kordula, The essential Apostol spectrum and finite dimensional perturbations, to appear. Zbl0880.47005
- [9] V. Kordula and V. Müller, The distance from the Apostol spectrum, to appear. Zbl0861.47008
- [10] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105. Zbl0694.47002
- [11] M. Mbekhta et A. Ouahab, Opérateur s-régulier dans un espace de Banach et théorie spectrale, Publ. Inst. Rech. Math. Av. Lille 22 (1990), XII.
- [12] M. Mbekhta et A. Ouahab, Contribution à la théorie spectrale généralisée dans les espaces de Banach, C. R. Acad. Sci. Paris 313 (1991), 833-836. Zbl0742.47001
- [13] V. Müller, On the regular spectrum, J. Operator Theory 31 (1994), 363-380. Zbl0845.47005
- [14] V. Rakočević, Generalized spectrum and commuting compact perturbations, Proc. Edinburgh Math. Soc. 36 (1993), 197-209. Zbl0794.47003
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- [16] P. Saphar, Contributions à l'étude des aplications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363-384. Zbl0139.08502
- [17] C. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), 484-489.
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- [19] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148. Zbl0306.47014
- [20] F.-H. Vasilescu, Analytic functions and some residual spectral properties, Rev. Roumaine Math. Pures Appl. 15 (1970), 435-451. Zbl0194.44101
- [21] F.-H. Vasilescu, Spectral mapping theorem for the local spectrum, Czechoslovak Math. J. 30 (1980), 28-35. Zbl0437.47003
- [22] P. Vrbová, On local spectral properties of operators in Banach spaces, ibid. 23 (1973), 483-492. Zbl0268.47006
- [23] W. Żelazko, Axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261. Zbl0426.47002

## Citations in EuDML Documents

top- J. Koliha, M. Mbekhta, V. Müller, Pak Poon, Corrigendum and addendum: "On the axiomatic theory of spectrum II"
- M. Berkani, Dagmar Medková, A note on the index of $B$-Fredholm operators
- Angel Martínez Meléndez, Antoni Wawrzyńczyk, An approach to joint spectra
- M. Mbekhta, V. Müller, On the axiomatic theory of spectrum II
- Vladimír Müller, Axiomatic theory of spectrum III: semiregularities
- M. Berkani, Restriction of an operator to the range of its powers
- Jacobus J. Grobler, Heinrich Raubenheimer, Andre Swartz, The index for Fredholm elements in a Banach algebra via a trace II
- M. Berkani, N. Castro, S. V. Djordjević, Single valued extension property and generalized Weyl’s theorem
- Vladimír Kordula, Vladimír Müller, Vladimir Rakočević, On the semi-Browder spectrum

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