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
DOI: https://doi.org/10.1090/S0002-9939-1977-0467377-X
MathSciNet review: 0467377
Full-text PDF

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] P. Enflo and H. P. Rosenthal, Some results concerning $ {L^p}(\mu )$-spaces, J. Functional Analysis 14 (1973), 325-348. MR 0350402 (50:2895)
  • [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] W. Howard, $ \mathcal{F}$-singular and $ \mathcal{F}$-cosingular operators, Colloq. Math. 22 (1970), 85-89. MR 0275194 (43:951)
  • [4] W. B. Johnson and E. Odell, Subspaces of $ {L_p}$ which embed into $ {l_p}$, Compositio Math. 28 (1974), 37-49. MR 0352938 (50:5424)
  • [5] J. Lindenstrauss, On some subspaces of $ {l^1}$ and $ {c_0}$, Bull. Res. Council of Israel 10 (1961), 74-80. MR 0187059 (32:4514)
  • [6] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., vol. 338, Springer-Verlag, Berlin and New York, 1973. MR 0415253 (54:3344)
  • [7] V. D. Milman, Some properties of strictly singular operators, Functional Anal. Appl. 3 (1969), 77-78. MR 0241997 (39:3332)
  • [8] A. Pietsch, Theorie der Operatorenideale, Wissenschaftliche Beiträge der Uni. Jena, 1972. MR 0361822 (50:14267)
  • [9] A. Pelczynski, On strictly singular and cosingular operators, I, II. Bull. Acad. Polon. Sci. 13 (1965), 31-41. MR 0177300 (31:1563)
  • [10] A. Pelczynski and H. P. Rosenthal, Localization techniques in $ {L^p}$ spaces, Studia Math. 52 (1975), 265-289. MR 0361729 (50:14174)
  • [11] D. Przeworska-Rolewicz, Equations in linear spaces, Polska Akademia Nauk, Monografie, 1968.
  • [12] H. P. Rosenthal, On relatively disjoint families of measures with applications to Banach space theory, Studia Math. 37 (1970), 13-36. MR 0270122 (42:5015)
  • [13] H. L. Royden, Real analysis, Macmillan, New York. MR 0151555 (27:1540)
  • [14] L. Tzafriri, Remarks on contractive projections in $ {L_p}$-spaces, Israel J. Math. 7 (1969), 9-15. MR 0248514 (40:1766)

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

American Mathematical Society