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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 10, Pages 3–15 (Mi ivm8833)  
This article is cited in 7 scientific papers (total in 7 papers)

On some functional calculus of closed operators in a Banach space

A. A. Atvinovskii, A. R. Mirotin

Chair of Mathematical Analysis, F. Skorina Gomel State University, 104 Sovetskaya str., Gomel, 246019 Republic of Belarus
Full-text PDF (221 kB) Citations (7)
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Abstract: We develop a functional calculus of closed operators in a Banach space based on the class of functions in the form $1/g$, where $g$ belongs to the class $R[a,b]$ introduced by M. G. Krein. We prove continuity, stability, uniqueness, spectral mapping, and inverse operator theorems and describe some other properties of the considered calculus.
Keywords: Krein class, operator monotone function, closed operator, functional calculus.
Received: 30.06.2012
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 10, Pages 1–12
DOI: https://doi.org/10.3103/S1066369X13100010
Bibliographic databases:
Document Type: Article
UDC: 517.984
Language: Russian
Citation: A. A. Atvinovskii, A. R. Mirotin, “On some functional calculus of closed operators in a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 10, 3–15; Russian Math. (Iz. VUZ), 57:10 (2013), 1–12
Citation in format AMSBIB
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\by A.~A.~Atvinovskii, A.~R.~Mirotin
\paper On some functional calculus of closed operators in a~Banach space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 10
\pages 3--15
\mathnet{http://mi.mathnet.ru/ivm8833}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 10
\pages 1--12
\crossref{https://doi.org/10.3103/S1066369X13100010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84885574598}
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    Cycle of papers
    This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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