Geodesic
Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 19-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the real Banach space we consider linear bounded invertible operator, norms of powers of which satisfy the condition of nonquasianalyticity. For this operator, we obtain conditions of existence of non-trivial invariant subspace and decomposability (in Foias sense).
Keywords: the real Banach space, operator spectrum, invariant subspaces, Beurling spectrum, decomposable (in Foias sense) operator. 
@article{VNGU_2014_14_3_a1,
     author = {E. E. Dikarev and D. M. Polyakov},
     title = {Harmonic {Analysis} of {Nonquasianalytic} {Operators} in {Real} {Banach} {Space}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {19--28},
     year = {2014},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a1/}
}
TY  - JOUR
AU  - E. E. Dikarev
AU  - D. M. Polyakov
TI  - Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2014
SP  - 19
EP  - 28
VL  - 14
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a1/
LA  - ru
ID  - VNGU_2014_14_3_a1
ER  - 
%0 Journal Article
%A E. E. Dikarev
%A D. M. Polyakov
%T Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2014
%P 19-28
%V 14
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a1/
%G ru
%F VNGU_2014_14_3_a1
E. E. Dikarev; D. M. Polyakov. Harmonic Analysis of Nonquasianalytic Operators in Real Banach Space. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 3, pp. 19-28. http://geodesic.mathdoc.fr/item/VNGU_2014_14_3_a1/

[1] Baskakov A. G., Zagorskii A. S., “Spectral theory of linear relations on real Banach spaces”, Mathematical Notes, 81:1 (2007), 15–27 | DOI | DOI

[2] Lyubich Yu. I., Introduction to the Theory of Banach Representations of Groups, Birkhäuser Verlag, 1988

[3] Domar Y., Lindahl L.-A., “Three Spectral Notions for Representations of Commutative Banach Algebras”, Ann. Inst. Fourier. Grenoble, 25:2 (1975), 1–32 | DOI

[4] Lyubich Yu. I., Matsaev V. I., Feldman G. M., “On representations with a separable spectrum”, Functional Analysis and Its Applications, 7:2 (1973), 129–136 | DOI

[5] Baskakov A. G., “Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators”, J. of Math. Sci., 137:4 (2006), 4885–5036 | DOI

[6] Dunford N., Schwartz J. T., Linear Operators, v. 3, Spectral operators, John Wiley and Sons Inc., New York, 1988

[7] Colojoara I., Foias C., Theory of Generalized Spectral Operators, Gordon and Breach, N. Y., 1968

[8] H. Garth Dales et al. (eds.), Introduction to Banach Algebras, Operators, and Harmonic Analysis, Cambridge University Press, Cambridge, 2003

[9] Baskakov A. G., “Harmonic analysis of cosine and exponential operator-valued functions”, Mathematics of the USSR-Sbornik, 52:1 (1985), 63–90 | DOI

[10] Baskakov A. G., “Spectral synthesis in Banach modules over commutative Banach algebras”, Mathematical Notes, 34:4 (1983), 776–782 | DOI

[11] Baskakov A. G., “Inequalities of Bernshtein type in abstract harmonic analysis”, Sib. Mat. J., 20:5 (1979), 665–672 | DOI

[12] Shilov G., “On regular normed rings”, Travaux Inst. Math. Stekloff, 21, Acad. Sci. USSR, M.–Leningrad, 1947, 3–118 (in Russian)

[13] Kaniuth E., A Course in Commutative Banach Algebras, Springer, N. Y., 2009

[14] Storozhuk K. V., “Symmetric Invariant Subspaces of Complexifications of Linear Operators”, Math. Notes, 91:4 (2012), 597–599 | DOI | DOI