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)

 
 

 

Tauberian operators on Banach spaces


Authors: Nigel Kalton and Albert Wilansky
Journal: Proc. Amer. Math. Soc. 57 (1976), 251-255
MSC: Primary 47B05; Secondary 47B30
DOI: https://doi.org/10.1090/S0002-9939-1976-0473896-1
MathSciNet review: 0473896
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Tauberian operator: $ E \to F$ (Banach spaces) is one which satisfies $ T''g \in F,g \in E''$ imply $ g \in E$. The action of such operators and their pre-images on compact sets is studied in order to compare ``Tauberian'' with ``weakly compact", an opposite property. Properties related to range closed are introduced which force operators with Tauberian-like properties to be Tauberian. Classes of spaces appear for which Tauberian is equivalent to semi-Fredholm. One example of this is the historical reason for the definition of these operators.


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

  • [1] W. G. Bade and P. C. Curtis, Jr., Embedding theorems for commutative Banach algebras, Pacific J. Math. 18 (1966), 391-409. MR 34 #1878. MR 0202001 (34:1878)
  • [2] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series, Studia Math. 17 (1958), 151-164. MR 22 #5872. MR 0115069 (22:5872)
  • [3] W. J. Davis, T. Figiel, W. B. Johnson and P. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311-327. MR 0355536 (50:8010)
  • [4] R. de Vos, $ \theta $ maps between FK spaces, Math Z. 129 (1975), 287-298.
  • [5] D. J. H. Garling and A. Wilansky, On a summability theorem of Berg, Crawford and Whitley, Proc. Cambridge Philos. Soc. 71 (1972), 495-197. MR 45 #4014. MR 0294946 (45:4014)
  • [6] A. Lebow and M. Schechter, Semigroups of operators and measures of noncompactness, J. Functional Analysis 7 (1971), 1 26. MR 42 #8301. MR 0273422 (42:8301)
  • [7] H. P. Rosenthal, A characterization of Banach spaces containing $ {l^1}$, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411-2413. MR 0358307 (50:10773)
  • [8] M. Schechter, Principles of functional analysis, Academic Press, New York, 1971. MR 0445263 (56:3607)
  • [9] A. Wilansky, Semi-Fredholm maps of FK spaces, Math. Z. 144 (1975), 9-12. MR 0405155 (53:8950)
  • [10] K.-W. Yang, The generalized Fredholm operators, Trans. Amer. Math. Soc. 216 (1976), 313-326. MR 0423114 (54:11095)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B05, 47B30

Retrieve articles in all journals with MSC: 47B05, 47B30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0473896-1
Keywords: Tauberian, operators, Banach space
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society