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DOI: 10.23671/VNC.2012.14.11013

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
Language: English Download the full text  
For citation: Smirnov E. I. Using homological methods on the base of iterated spectra in functional analysis. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], 2012, vol. 14, no. 4, pp.73-82. DOI 10.23671/VNC.2012.14.11013


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