The mappings of degree 1

Maria N. Krein

Abstract and Applied Analysis, 2006, vol. 2006, issue 1

Abstract: The maps of the form f(x)=∑i=1nai·x·bi, called 1‐degree maps, are introduced and investigated. For noncommutative algebras and modules over them 1‐degree maps give an analogy of linear maps and differentials. Under some conditions on the algebra 𝒜, contractibility of the group of 1‐degree isomorphisms is proved for the module l2(𝒜). It is shown that these conditions are fulfilled for the algebra of linear maps of a finite‐dimensional linear space. The notion of 1‐degree map gives a possibility to define a nonlinear Fredholm map of l2(𝒜) and a Fredholm manifold modelled by l2(𝒜). 1‐degree maps are also applied to some problems of Markov chains.

Date: 2006
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https://doi.org/10.1155/AAA/2006/90837

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2006:y:2006:i:1:n:090837

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