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Mat. Zametki, 1998, Volume 64, Issue 3, Pages 423–430 (Mi mz1413)  

This article is cited in 8 scientific papers (total in 8 papers)

Functions from the Schoenberg class $\mathscr T$ act in the cone of dissipative elements of a Banach algebra. II

A. R. Mirotin

Francisk Skorina Gomel State University

Abstract: The functional calculus of several commuting dissipative elements of a complex Banach algebra with identity, first introduced in the preceding work by the author, is developed. Uniqueness, continuity, and stability theorems, composite function theorems, and a formula for the resolvent are established. Applications to the theory of sectorial operators in Hilbert space are given.

DOI: https://doi.org/10.4213/mzm1413

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English version:
Mathematical Notes, 1998, 64:3, 364–370

Bibliographic databases:

UDC: 517
Received: 01.08.1997

Citation: A. R. Mirotin, “Functions from the Schoenberg class $\mathscr T$ act in the cone of dissipative elements of a Banach algebra. II”, Mat. Zametki, 64:3 (1998), 423–430; Math. Notes, 64:3 (1998), 364–370

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. R. Mirotin, “O mnogomernom funktsionalnom ischislenii Bokhnera-Fillipsa”, PFMT, 2009, no. 1(1), 60–63  mathnet
    2. A. R. Mirotin, “On some properties of the multidimensional Bochner–Phillips functional calculus”, Siberian Math. J., 52:6 (2011), 1032–1041  mathnet  crossref  mathscinet  isi
    3. A. R. Mirotin, “A Joint Spectral Mapping Theorem for Sets of Semigroup Generators”, Funct. Anal. Appl., 46:3 (2012), 210–217  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. R. Mirotin, “Properties of Bernstein Functions of Several Complex Variables”, Math. Notes, 93:2 (2013), 257–265  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. A. R. Mirotin, “On a Class of Operator Monotone Functions of Several Variables”, Math. Notes, 94:1 (2013), 160–163  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. A. R. Mirotin, “On joint spectra of families of unbounded operators”, Izv. Math., 79:6 (2015), 1235–1259  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Mirotin A.R., “Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations”, Oper. Matrices, 11:1 (2017), 199–217  crossref  mathscinet  zmath  isi  scopus
    8. Mirotin A.R., “Bernstein Functions of Several Semigroup Generators on Banach Spaces Under Bounded Perturbations, II”, Oper. Matrices, 12:2 (2018), 445–463  crossref  mathscinet  zmath  isi
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