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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 401, Pages 93–102 (Mi znsl5228)  
On regulariziers of unbounded linear operators in Banach spaces

V. M. Kaplitskiiab

a Southern Federal University, Rostov-on-Don, Russia
b South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
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Abstract: Regulariziers of densely defined unbounded linear operators in Banach spaces and their applications to spectral theory are considered. Necessary and sufficient conditions in terms of regularizier properties for an unbounded operator $T$ to be discrete are obtained. In the case when $T$ has a selfadjoint regularizier in some Schatten–von Neumann ideals, asymptotic properties of the eigenvalues are investigated, namely, it is shown that the eigenvalues of $T$ asymptotically belong to a some angle in the complex plane.
Key words and phrases: regularizier, canonical regularizier, Shatten–von-Neimann ideal, discretness of spectrum.
Received: 16.07.2012
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 194, Issue 6, Pages 651–655
DOI: https://doi.org/10.1007/s10958-013-1554-8
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: V. M. Kaplitskii, “On regulariziers of unbounded linear operators in Banach spaces”, Investigations on linear operators and function theory. Part 40, Zap. Nauchn. Sem. POMI, 401, POMI, St. Petersburg, 2012, 93–102; J. Math. Sci. (N. Y.), 194:6 (2013), 651–655
Citation in format AMSBIB
\Bibitem{Kap12}
\by V.~M.~Kaplitskii
\paper On regulariziers of unbounded linear operators in Banach spaces
\inbook Investigations on linear operators and function theory. Part~40
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 401
\pages 93--102
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5228}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2981969}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 194
\issue 6
\pages 651--655
\crossref{https://doi.org/10.1007/s10958-013-1554-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84898942670}
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