Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On perturbations of Fredholm operators in $ L\sb{p}(\mu )$-spaces


Author: L. Weis
Journal: Proc. Amer. Math. Soc. 67 (1977), 287-292
MSC: Primary 47B30; Secondary 47A55
MathSciNet review: 0467377
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Answering a question of Milman, we show that a continuous linear operator $ T:{L_p}(\mu ) \to {L_p}(\mu ),1 < p < 2$, is a Fredholm perturbation iff T is strictly singular.


References [Enhancements On Off] (What's this?)

  • [1] Per Enflo and Haskell P. Rosenthal, Some results concerning 𝐿^{𝑝}(𝜇)-spaces, J. Functional Analysis 14 (1973), 325–348. MR 0350402
  • [2] I. Gohberg, A. Markus, and I. Feldman, Normally solvable operators and ideals associated with them, Amer. Math. Soc. Transl. (2) 61 (1967), 63-84.
  • [3] Joe Howard, \cal𝐹-singular and \cal𝐺-cosingular operators, Colloq. Math. 22 (1970), 85–89 (errata insert). MR 0275194
  • [4] W. B. Johnson and E. Odell, Subspaces of 𝐿_{𝑝} which embed into 𝑙_{𝑝}, Compositio Math. 28 (1974), 37–49. MR 0352938
  • [5] Joram Lindenstrauss, On some subspaces of 𝑙¹ and 𝑐₀, Bull. Res. Council Israel Sect. F 10F (1961), 74–80. MR 0187059
  • [6] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
  • [7] V. D. Mil′man, Certain properties of strictly singular operators, Funkcional. Anal. i Priložen. 3 (1969), no. 1, 93–94 (Russian). MR 0241997
  • [8] Albrecht Pietsch, Theorie der Operatorenideale (Zusammenfassung), Friedrich-Schiller-Universität, Jena, 1972 (German). Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena. MR 0361822
  • [9] A. Pełczyński, On strictly singular and strictly cosingular operators. I. Strictly singular and strictly cosingular operators in 𝐶(𝑆)-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 31–36. MR 0177300
  • [10] A. Pełczyński and H. P. Rosenthal, Localization techniques in 𝐿^{𝑝} spaces, Studia Math. 52 (1974/75), 263–289. MR 0361729
  • [11] D. Przeworska-Rolewicz, Equations in linear spaces, Polska Akademia Nauk, Monografie, 1968.
  • [12] Haskell P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13–36. MR 0270122
  • [13] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
  • [14] L. Tzafriri, Remarks on contractive projections in 𝐿_{𝑝}-spaces, Israel J. Math. 7 (1969), 9–15. MR 0248514

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B30, 47A55

Retrieve articles in all journals with MSC: 47B30, 47A55


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0467377-X
Keywords: $ {L_p}(\mu )$-spaces, Fredholm perturbation
Article copyright: © Copyright 1977 American Mathematical Society