Using homological methods on the base of iterated spectra in functional analysis

Smirnov E. I.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 4.

Abstract:
We introduce new concepts of functional analysis: Hausdorff spectrum and Hausdorff limit or \(H\)-limit of Hausdorff spectrum of locally convex spaces. Particular cases of regular \(H\)-limit are projective and inductive limits of separated locally convex spaces. The class of \(H\)-spaces contains Frechet spaces and is stable under forming countable inductive and projective limits, closed subspaces and  quotient spaces. Moreover, for \(H\)-space an unproved variant of the closed graph theorem holds true. Homological methods are used for proving of theorems of vanishing at zero for first derivative of Hausdorff limit functor: \(\Haus^{1}(\textbf{\textit{X}})=0\).

Keywords: topology, spectrum, closed graph theorem, differential equation, homological methods, category

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