Geodesic
On some functional calculus of closed operators in a~Banach space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 3-15

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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. 
@article{IVM_2013_10_a0,
     author = {A. A. Atvinovskii and A. R. Mirotin},
     title = {On some functional calculus of closed operators in {a~Banach} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--15},
     publisher = {mathdoc},
     number = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_10_a0/}
}
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A. A. Atvinovskii; A. R. Mirotin. On some functional calculus of closed operators in a~Banach space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2013), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2013_10_a0/