Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

AVERAGES AND COMPACT, ABSOLUTELY SUMMING AND NUCLEAR OPERATORS ON C (Ω)

  • Popa, Dumitru (DEPARTMENT OF MATHEMATICS UNIVERSITY OF CONSTANTA)
  • Received : 2008.06.20
  • Published : 2010.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

Keywords

References

  1. A. Defant and K. Floret, Tensor Norms and Operators Ideals, North-Holland Mathematics Studies, 176. North-Holland Publishing Co., Amsterdam, 1993.
  2. J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, 43. Cambridge University Press, Cambridge, 1995.
  3. J. Diestel and J. J. Uhl, Vector Measures, Mathematical Surveys, No. 15. American Mathematical Society, Providence, R.I., 1977.
  4. L. Drewnowski and Z. Lipecki, On vector measures which have everywhere infinite variation or noncompact range, Dissertationes Math. (Rozprawy Mat.) 339 (1995), 39 pp.
  5. R. Latala and K. Oleszkiewicz, On the best constant in the Khinchin-Kahane inequality, Studia Math. 109 (1994), no. 1, 101-104.
  6. A. Pietsch, Eigenvalues and s-numbers, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987.
  7. A. Pietsch and J. Wenzel, Orthonormal Systems and Banach Space Geometry, Encyclopedia of Mathematics and its Applications, 70. Cambridge University Press, Cambridge, 1998.
  8. D. Popa, Examples of operators on C[0, 1] distinguishing certain operator ideals, Arch. Math. (Basel) 88 (2007), no. 4, 349-357. https://doi.org/10.1007/s00013-006-1916-2
  9. N. Tomczak-Jagermann, Banach-Mazur distances and finite dimensional operator ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 38, Harlow: Longman Scientific & Technical; New York: John Wiley & Sons, Inc., 1989.

Cited by

  1. When does a kernel generate a nuclear operator? vol.38, pp.4, 2015, https://doi.org/10.2989/16073606.2014.981718
  2. The summing nature of the multiplication operator from $$l_{p}\left( \mathcal {X}\right) $$ l p X into $$ c_{0}\left( \mathcal {Y}\right) $$ c 0 Y 2018, https://doi.org/10.1007/s13398-016-0370-7
  3. Copies of in pp.1563-5139, 2019, https://doi.org/10.1080/03081087.2018.1429379