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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 6, Pages 145–170 (Mi izv8262)  

This article is cited in 4 scientific papers (total in 4 papers)

On joint spectra of families of unbounded operators

A. R. Mirotin

Francisk Skorina Gomel State University

Abstract: We consider several types of joint spectra of a finite set of commuting closed operators in a Banach space. We establish new relations between these spectra (it was previously known only that the Taylor spectrum is contained in the commutant spectrum) and prove spectral mapping theorems in the case of generators of semigroups. Some of these theorems generalize previous results of the author. The results obtained are applied to stability issues for multi-parameter semigroups.

Keywords: unbounded operator, joint spectrum, Bernstein function, Bochner–Philips functional calculus, spectral mapping theorem, multi-parameter operator semigroup, uniform stability, strong stability, abstract Cauchy problem.

DOI: https://doi.org/10.4213/im8262

Full text: PDF file (664 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:6, 1235–1259

Bibliographic databases:

UDC: 517.986.7+517.984.3
MSC: 47A10, 47A60, 47D03
Received: 09.06.2014
Revised: 12.04.2015

Citation: A. R. Mirotin, “On joint spectra of families of unbounded operators”, Izv. RAN. Ser. Mat., 79:6 (2015), 145–170; Izv. Math., 79:6 (2015), 1235–1259

Citation in format AMSBIB
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  • https://doi.org/10.4213/im8262
  • http://mi.mathnet.ru/eng/izv/v79/i6/p145

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ricci F., Wrobel B., “Spectral Multipliers For Functions of Fixed K-Type on Lp(Sl(2,R))”, Math. Nachr.  crossref  isi
    2. A. R. Mirotin, “Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations”, Oper. Matrices, 11:1 (2017), 199–217  crossref  mathscinet  zmath  isi  scopus
    3. A. R. Mirotin, “Corrections and Complements to My Paper “On a Class of Operator Monotone Functions of Several Variables””, Math. Notes, 101:6 (2017), 1061–1065  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. R. Mirotin, “Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations, II”, Oper. Matrices, 12:2 (2018), 445–463  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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