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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.
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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