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1997 | 122 | 2 | 131-137
Tytuł artykułu

Semi-Browder operators and perturbations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An operator in a Banach space is called upper (resp. lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (resp. descent). An operator in a Banach space is called semi-Browder if it is upper semi-Browder or lower semi-Browder. We prove the stability of the semi-Browder operators under commuting Riesz operator perturbations. As a corollary we get some results of Grabiner [6], Kaashoek and Lay [8], Lay [11], Rakočević [15] and Schechter [16].
Słowa kluczowe
Czasopismo
Rocznik
Tom
122
Numer
2
Strony
131-137
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-08-04
poprawiono
1996-07-12
Twórcy
  • Department of Mathematics, Faculty of Philosophy, University of Niš, Cirila and Metodija 2, 18000 Niš, Serbia, Yugoslavia, vrakoc@ban.junis.ni.ac.yu
Bibliografia
  • [1] S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Marcel Dekker, 1974.
  • [2] A. S. Faĭnshteĭn, On measures of noncompactness of linear operators and analogs of the minimum modulus for semi-Fredholm operators, Spektr. Teor. Oper. 6, Èlm, Baku, 1985, 182-195 (in Russian).
  • [3] M. A. Goldman and S. N. Kračkovskiĭ, Behaviour of the space of zero elements with finite-dimensional salient on the Riesz kernel under perturbations of the operator, Dokl. Akad. Nauk SSSR 221 (1975), 532-534 (in Russian); English transl.: Soviet Math. Dokl. 16 (1975), 370-373.
  • [4] M. González and A. Martinón, Operational quantities derived from the norm and measures of non-compactness, Proc. Roy. Irish Acad. Sect. A 91 (1991), 63-70.
  • [5] M. González and A. Martinón, Operational quantities characterizing semi-Fredholm operators, Studia Math. 114 (1995), 13-27.
  • [6] S. Grabiner, Ascent, descent, and compact perturbations, Proc. Amer. Math. Soc. 71 (1978), 79-80.
  • [7] R. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, 1988.
  • [8] M. A. Kaashoek and D. C. Lay, Ascent, descent, and commuting perturbations, Trans. Amer. Math. Soc. 186 (1972), 35-47.
  • [9] V. Kordula, V. Müller and V. Rakočević, On the semi-Browder spectrum, Studia Math., to appear.
  • [10] H. Kroh and P. Volkmann, Störungssätze für Semifredholmoperatoren, Math. Z. 148 (1976), 295-297.
  • [11] D. Lay, Characterizations of the essential spectrum of F. E. Browder, Bull. Amer. Math. Soc. 74 (1968), 246-248.
  • [12] A. Martinón, Cantidades operacionales en teoría de Fredholm, Doctoral thesis, University of La Laguna, 1989.
  • [13] V. Müller, The inverse spectral radius formula and removability of spectrum, Časopis Pěst. Mat. 108 (1983), 412-415.
  • [14] V. Rakočević, Approximate point spectrum and commuting compact perturbations, Glasgow Math. J. 28 (1986), 193-198.
  • [15] V. Rakočević, Semi-Fredholm operators with finite ascent or descent and perturbations, Proc. Amer. Math. Soc. 123 (1995), 3823-3825.
  • [16] M. Schechter, On perturbations of essential spectra, J. London Math. Soc. (2) 1 (1969), 343-347.
  • [17] H.-O. Tylli, On the asymptotic behaviour of some quantities related to semiFredholm operators, J. London Math. Soc. (2) 31 (1985), 340-348.
  • [18] H.-O. Tylli, On semi-Fredholm operators, Calkin algebras and some related quantities, Academic dissertation, Helsinki, Department of Mathematics, University of Helsinki, 1986.
  • [19] T. T. West, A Riesz-Schauder theorem for semi-Fredholm operators, Proc. Roy. Irish Acad. Sect. A 87 (1987), 137-146.
  • [20] J. Zemánek, The semi-Fredholm radius of a linear operator, Bull. Polish Acad. Sci. Math. 32 (1984), 67-76.
  • [21] J. Zemánek, Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219-234.
  • [22] J. Zemánek, Compressions and the Weyl-Browder spectra, Proc. Roy. Irish Acad. Sect. A 86 (1986), 57-62.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv122i2p131bwm
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