Geodesic
On some functional calculus of closed operators in a~Banach space.~II
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 3-16

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We develop a functional calculus for a class of closed operators in Banach space. We establish several properties of the calculus under consideration such as continuity, stability, the uniqueness theorem, the spectral mapping theorem, the inversion theorem and some others. In the authors' preceding work the analogous functional calculus was developed for more narrow class of operators.
Keywords: Markov function, Krein class, functional calculus, Hirsch functional calculus, closed operator. 
@article{IVM_2015_5_a0,
     author = {A. A. Atvinovskii and A. R. Mirotin},
     title = {On some functional calculus of closed operators in {a~Banach} {space.~II}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--16},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_5_a0/}
}
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A. A. Atvinovskii; A. R. Mirotin. On some functional calculus of closed operators in a~Banach space.~II. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 3-16. http://geodesic.mathdoc.fr/item/IVM_2015_5_a0/