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1996 | 119 | 2 | 109-128
Tytuł artykułu

On the axiomatic theory of spectrum

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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).
Czasopismo
Rocznik
Tom
119
Numer
2
Strony
109-128
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-04-19
poprawiono
1995-11-20
Twórcy
autor
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
autor
  • Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic , vmuller@mbox.cesnet.cz
Bibliografia
  • [1] C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1985), 279-294.
  • [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973.
  • [3] R. E. Curto and A. T. Dash, Browder spectral systems, Proc. Amer. Math. Soc. 103 (1988), 407-413.
  • [4] N. Dunford, Survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217-274.
  • [5] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17-32.
  • [6] J. D. Gray, Local analytic extensions of the resolvent, Pacific J. Math. 27 (1968), 305-324.
  • [7] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
  • [8] V. Kordula, The essential Apostol spectrum and finite dimensional perturbations, to appear.
  • [9] V. Kordula and V. Müller, The distance from the Apostol spectrum, to appear.
  • [10] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105.
  • [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.
  • [13] V. Müller, On the regular spectrum, J. Operator Theory 31 (1994), 363-380.
  • [14] V. Rakočević, Generalized spectrum and commuting compact perturbations, Proc. Edinburgh Math. Soc. 36 (1993), 197-209.
  • [15] T. J. Ransford, Generalized spectra and analytic multivalued functions, J. London Math. Soc. 29 (1984), 306-322.
  • [16] P. Saphar, Contributions à l'étude des aplications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363-384.
  • [17] C. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), 484-489.
  • [18] C. Schmoeger, Relatively regular operators and a spectral mapping theorem, J. Math. Anal. Appl. 175 (1993), 315-320.
  • [19] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148.
  • [20] F.-H. Vasilescu, Analytic functions and some residual spectral properties, Rev. Roumaine Math. Pures Appl. 15 (1970), 435-451.
  • [21] F.-H. Vasilescu, Spectral mapping theorem for the local spectrum, Czechoslovak Math. J. 30 (1980), 28-35.
  • [22] P. Vrbová, On local spectral properties of operators in Banach spaces, ibid. 23 (1973), 483-492.
  • [23] W. Żelazko, Axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv119i2p109bwm
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