Geodesic
On hyponormal operators in Krein spaces
Archivum mathematicum, Tome 55 (2019) no. 4, pp. 249-259 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators $T$ for which there exists a fundamental decomposition $\mathbb{K}= \mathbb{K}^{+} \oplus \mathbb{K}^{-}$ of the Krein space $\mathbb{K}$ with $\mathbb{K}^{+}$ and $\mathbb{K}^{-}$ invariant under $T$.
In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators $T$ for which there exists a fundamental decomposition $\mathbb{K}= \mathbb{K}^{+} \oplus \mathbb{K}^{-}$ of the Krein space $\mathbb{K}$ with $\mathbb{K}^{+}$ and $\mathbb{K}^{-}$ invariant under $T$.
DOI : 10.5817/AM2019-4-249
Classification : 46C20, 47B50
Keywords: Hyponormal operators; Krein spaces; $J$-hyponormal operators 
@article{10_5817_AM2019_4_249,
     author = {Esmeral, Kevin and Ferrer, Osmin and Jalk, Jorge and Lora Castro, Boris},
     title = {On hyponormal operators in {Krein} spaces},
     journal = {Archivum mathematicum},
     pages = {249--259},
     year = {2019},
     volume = {55},
     number = {4},
     doi = {10.5817/AM2019-4-249},
     mrnumber = {4038360},
     zbl = {07144740},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-249/}
}
TY  - JOUR
AU  - Esmeral, Kevin
AU  - Ferrer, Osmin
AU  - Jalk, Jorge
AU  - Lora Castro, Boris
TI  - On hyponormal operators in Krein spaces
JO  - Archivum mathematicum
PY  - 2019
SP  - 249
EP  - 259
VL  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-249/
DO  - 10.5817/AM2019-4-249
LA  - en
ID  - 10_5817_AM2019_4_249
ER  - 
%0 Journal Article
%A Esmeral, Kevin
%A Ferrer, Osmin
%A Jalk, Jorge
%A Lora Castro, Boris
%T On hyponormal operators in Krein spaces
%J Archivum mathematicum
%D 2019
%P 249-259
%V 55
%N 4
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2019-4-249/
%R 10.5817/AM2019-4-249
%G en
%F 10_5817_AM2019_4_249
Esmeral, Kevin; Ferrer, Osmin; Jalk, Jorge; Lora Castro, Boris. On hyponormal operators in Krein spaces. Archivum mathematicum, Tome 55 (2019) no. 4, pp. 249-259. doi: 10.5817/AM2019-4-249

[1] Andô, T.: On hyponormal operators. Proc. Amer. Math. Soc. 14 (1963), 290–291. | DOI | MR

[2] Azizov, T.Ya., Iokhvidov, I.S.: Linear operator in spaces with an indefinite metric. Pure and Applied Mathematics, John Wiley $\&$ Sons, 1989. | MR

[3] Berberian, S.K.: Introduction to Hilbert space. Oxford University Press, 1961. | MR

[4] Bognar, J.: Indefinite inner product spaces. Springer, 1974. | MR

[5] Braha, N.L., Lohaj, M., Marevci, F.H., Lohaj, Sh.: Some properties of paranormal and hyponormal operators. Bull. Math. Anal. Appl. 1 (2) (2009), 23–35. | MR

[6] Cowen, C.C., Shaokuan, L.: Hilbert space operators that are subnormal in the Krein space sense. J. Operator Theory 20 (1988), 165–181. | MR

[7] Esmeral, K., Ferrer, O., Castro, B. Lora: Dual and similar frames in Krein spaces. Int. J. Math. Anal. 19 (2016), 939–952. | DOI

[8] Halmos, P.R.: Normal dilations and extensions of operators. Summa Brasil. Math. 2 (1950), 125–134. | MR

[9] McEnnis, B.W.: Fundamental reducibility of selfadjoint operators on Krein space. J. Operator Theory 8 (1982), 219–225. | MR

[10] Putnam, C.R.: On semi-normal operators. Pacific J. Math. 7 (1957), 1649–1652. | DOI | MR

[11] Sheth, I.H.: On hyponormal operators. Proc. Amer. Math. Soc. 17 (1966), 998–1000. | DOI | MR

[12] Stampfli, J.G.: Hyponormal operators. Pacific J. Math. 12 (1962), 1453–1458. | DOI | MR

[13] Xia, D.: Spectral theory of hyponormal operators. Birkhäuser Verlag, 1983. | MR

Cité par Sources :