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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 5, Pages 915–941 (Mi izv1431)  

This article is cited in 9 scientific papers (total in 9 papers)

On spectral properties of operators with a shift

A. B. Antonevich, A. V. Lebedev


Abstract: A formula is obtained for the spectral radius of a weighted shift operator for a broad class of spaces in the case of an arbitrary invertible shift, and some general theorems are proved about properties of the spectrum for such operators. Necessary and sufficient conditions are found for invertibility of two-term operators with a shift.
Bibliography: 39 titles.

Full text: PDF file (2488 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 23:2, 201–224

Bibliographic databases:

UDC: 517.983.23+517.984.5
MSC: Primary 47A10, 47B37; Secondary 47A35, 57R50, 58F09, 58F11

Citation: A. B. Antonevich, A. V. Lebedev, “On spectral properties of operators with a shift”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983), 915–941; Math. USSR-Izv., 23:2 (1984), 201–224

Citation in format AMSBIB
\Bibitem{AntLeb83}
\by A.~B.~Antonevich, A.~V.~Lebedev
\paper On spectral properties of operators with a~shift
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 5
\pages 915--941
\mathnet{http://mi.mathnet.ru/izv1431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=718411}
\zmath{https://zbmath.org/?q=an:0558.47023|0541.47027}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 23
\issue 2
\pages 201--224
\crossref{https://doi.org/10.1070/IM1984v023n02ABEH001464}


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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. A. B. Antonevich, “On two methods of studying the invertibility of operators in $C^*$-algebras induced by dynamical systems”, Math. USSR-Sb., 52:1 (1985), 1–20  mathnet  crossref  mathscinet  zmath
    2. Abramovich I., Arenson E., Kitover A., “Operators in Banach C(K)-Modules and their Spectral Properties”, 301, no. 3, 1988, 525–528  mathscinet  isi
    3. A. B. Antonevich, “Boundary value problems with strong nonlocalness for elliptic equations”, Math. USSR-Izv., 34:1 (1990), 1–21  mathnet  crossref  mathscinet  zmath
    4. Karlovich I., “On Algebras of Singular Integral-Operators with Discrete-Groups of Shifts in Lp Spaces”, 304, no. 2, 1989, 274–280  zmath  isi
    5. A. K. Kitover, “Rotation operators with multiplication and some of their generalizations”, Funct. Anal. Appl., 24:1 (1990), 70–72  mathnet  crossref  mathscinet  zmath  isi
    6. Yu. D. Latushkin, A. M. Stepin, “Weighted translation operators and linear extensions of dynamical systems”, Russian Math. Surveys, 46:2 (1991), 95–165  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Campbell J., Latushkin Y., “Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators”, Commun. Math. Phys., 185:2 (1997), 379–396  crossref  mathscinet  zmath  adsnasa  isi
    8. Gundlach V., Latushkin Y., “A Sharp Formula for the Essential Spectral Radius of the Ruelle Transfer Operator on Smooth and Holder Spaces”, Ergod. Theory Dyn. Syst., 23:Part 1 (2003), 175–191  crossref  mathscinet  zmath  isi
    9. Antonevich A.B., Bakhtin V.I., Lebedev A.V., “On T-Entropy and Variational Principle for the Spectral Radii of Transfer and Weighted Shift Operators”, Ergod. Theory Dyn. Syst., 31:4 (2011), 995–1042  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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