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1998 | 131 | 3 | 271-287
Tytuł artykułu

On inessential and improjective operators.

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.
Czasopismo
Rocznik
Tom
131
Numer
3
Strony
271-287
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-09-30
poprawiono
1998-05-22
Twórcy
autor
  • Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy, paiena@unipa.it
  • Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain , gonzalem@ccaix3.unican.es
Bibliografia
  • [1] A P. Aiena, On Riesz and inessential operators, Math. Z. 201 (1989), 521-528.
  • [2] P. Aiena and M. González, Essentially incomparable Banach spaces and Fredholm theory, Proc. Roy. Irish Acad. Sect. A 93 (1993), 49-59.
  • [3] B. Beauzamy, Introduction to Banach Spaces and Their Geometry, 2nd ed., North-Holland, Amsterdam, 1985.
  • [4] G M. González, On essentially incomparable Banach spaces, Math. Z. 215 (1994), 621-629.
  • [5] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [6] H. G. Heuser, Functional Analysis, Wiley, Chichester, 1982.
  • [7] D. Kleinecke, Almost-finite, compact, and inessential operators, Proc. Amer. Math. Soc. 14 (1963), 863-868.
  • [8] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin, 1977.
  • [9] A. Pietsch, Inessential operators in Banach spaces, Integral Equations Operator Theory 1 (1978), 589-591.
  • [10] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.
  • [11] E. Tarafdar, Improjective operators and ideals in a category of Banach spaces, J. Austral. Math. Soc. 14 (1972), 274-292.
  • [12] E. Tarafdar, On further properties of improjective operators, ibid., 352-363.
  • [13] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, 1980.
  • [13] L. Weis, Perturbation classes of semi-Fredholm operators, Math. Z. 178 (1981), 429-442.
  • [15] R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252-261.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv131i3p271bwm
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