Lookup NU author(s): Dr Zinaida Lykova,
Dr Michael White
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We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex Χ of Banach spaces and continuous boundary maps dn with closed ranges and prove that Hn(Χ′) ≅ Hn(Χ)′, where Hn(Χ)′ is the dual space of the homology group of Χ and Hn(Χ′) is the cohomology group of the dual complex Χ′. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe explicitly the simplicial cohomology groups script H signn(ℓ1(ℤ+k), ℓ1 (ℤ+k)′) and homology groups script H signn(ℓ1(ℤ +k), ℓ1(ℤ+k)) of the semigroup algebra ℓ1(ℤ+k).
Author(s): Gourdeau F, Lykova ZA, White MC
Publication type: Article
Publication status: Published
Journal: Studia Mathematica
Print publication date: 01/01/2005
ISSN (print): 0039-3223
ISSN (electronic): 1730-6337
Publisher: Instytut Matematyczny Polska Akademia Nauk,
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