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Czasopismo
1996 | 119 | 2 | 129-147
Tytuł artykułu

On the axiomatic theory of spectrum II

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.
Czasopismo
Rocznik
Tom
119
Numer
2
Strony
129-147
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-03-03
poprawiono
1995-11-20
Twórcy
autor
autor
  • Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 11567 Praha 1, Czech Republic , vmuller@mbox.cesnet.cz
Bibliografia
  • [1] C. Apostol, The reduced minimum modulus, Michigan Math. J. 32(1985), 279-294.
  • [2] M. Berkani et A. Ouahab, Théorème de l'application spectrale pour le spectre essentiel quasi-Fredholm, Proc. Amer. Math. Soc., to appear.
  • [3] J. J. Buoni, R. Harte and T. Wickstead, Upper and lower Fredholm spectra, ibid. 66 (1977), 301-314.
  • [4] K. H. Förster and G.-O. Liebentrau, Semi-Fredholm operators and sequence conditions, Manuscripta Math. 44 (1983), 35-44.
  • [5] M. A. Gol'dman and S. N. Krachkovskiĭ, On the stability of some properties of a closed linear operator, Dokl. Akad. Nauk SSSR 209 (1973), 769-772 (in Russian); English transl.: Soviet Math. Dokl. 14 (1973), 502-505.
  • [6] S. Grabiner, Ascent, descent and compact perturbations, Proc. Amer. Math. Soc. 71 (1978), 79-80.
  • [7] S. Grabiner, Uniform ascent and descent of bounded operators, J. Math. Soc. Japan 34 (1982), 317-337.
  • [8] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971),17-32.
  • [9] R. Harte, Spectral mapping theorems, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89-107.
  • [10] M. A. Kaashoek, Stability theorems for closed linear operators, Indag. Math. 27 (1965), 452-466.
  • [11] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261-322.
  • [12] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin, 1966.
  • [13] V. Kordula, The essential Apostol spectrum and finite-dimensional perturbations, to appear.
  • [14] V. Kordula and V. Müller, The distance from the Apostol spectrum, Proc. Amer. Math, Soc., to appear.
  • [15] V. Kordula and V. Müller, On the axiomatic theory of spectrum, this issue, 109-128.
  • [16] J. P. Labrousse, Les opérateurs quasi-Fredholm : une généralisation des opérateurs semi-Fredholm, y Rend. Circ. Mat. Palermo 29 (1980), 161-258.
  • [17] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105.
  • [18] M. Mbekhta et A. Ouahab, Opérateur semi-régulier dans un espace de Banach et théorie spectrale, Acta Sci. Math. (Szeged), to appear.
  • [19] 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.
  • [20] V. Müller, On the regular spectrum, J. Operator Theory 31 (1994), 363-380.
  • [21] V. Rakočevič, Generalized spectrum and commuting compact perturbations, Proc. Edinburgh Math. Soc. 36 (1993), 197-208.
  • [22] B. N. Sadovskiĭ, Limit compact and condensing operators, Russian Math. Surveys 27 (1972), 85-155.
  • [23] P. Saphar, Contributions à l'étude des applications linéaires dans un espace de Banach, Bull. Soc. Math. France 92 (1964), 363-384.
  • [24] C. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), 484-489.
  • [25] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148.
  • [26] A. E. Taylor, Theorems on ascent, descent, nullity and defect of linear operators, Math. Ann. 163 (1966), 18-49.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv119i2p129bwm
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