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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

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

Banach spaces of continuous functions;weakly compact;compact;nuclear;p-summing

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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 2017, https://doi.org/10.1007/s13398-016-0370-7
  3. Copies of in pp.1563-5139, 2018, https://doi.org/10.1080/03081087.2018.1429379