Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE KÜNNETH SPECTRAL SEQUENCE FOR COMPLEXES OF BANACH SPACES

  • Park, HeeSook (Department of Mathematics Education Sunchon National University)
  • Received : 2017.07.10
  • Accepted : 2018.01.30
  • Published : 2018.07.01
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Abstract

In this paper, we form the basis of the abstract theory for constructing the $K{\ddot{u}}nneth$ spectral sequence for a complex of Banach spaces. As the category of Banach spaces is not abelian, several difficulties occur and hinder us from applying the usual method of homological algebra directly. The most notable facts are the image of a morphism of Banach spaces is not necessarily a Banach space, and also the closed summand of a Banach space need not be a topological direct summand. So, we consider some conditions and categorical terms that fit the category of Banach spaces to modify the familiar method of homological algebra.

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References

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