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Izvestiya: Mathematics, 2015, Volume 79, Issue 6, Pages 1235–1259
DOI: https://doi.org/10.1070/IM2015v079n06ABEH002779 (Mi im8262) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On joint spectra of families of unbounded operators

A. R. Mirotin

Francisk Skorina Gomel State University
English version PDF (404 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/IM2015v079n06ABEH002779
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.
Received: 09.06.2014
Revised: 12.04.2015
Bibliographic databases:
Document Type: Article
UDC: 517.986.7+517.984.3
MSC: 47A10, 47A60, 47D03
Language: English
Original paper language: Russian
Citation: A. R. Mirotin, “On joint spectra of families of unbounded operators”, Izv. Math., 79:6 (2015), 1235–1259
Citation in format AMSBIB
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\by A.~R.~Mirotin
\paper On joint spectra of families of unbounded operators
\jour Izv. Math.
\yr 2015
\vol 79
\issue 6
\pages 1235--1259
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Linking options:
  • https://www.mathnet.ru/eng/im8262
  • https://doi.org/10.1070/IM2015v079n06ABEH002779
  • https://www.mathnet.ru/eng/im/v79/i6/p145
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:574
    Russian version PDF:186
    English version PDF:20
    References:80
    First page:26
     
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