On hyponormal operators in Krein spaces
Kevin Esmeral; Osmin Ferrer; Jorge Jalk; Boris Lora Castro
Archivum Mathematicum (2019)
- Volume: 055, Issue: 4, page 249-259
- ISSN: 0044-8753
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topEsmeral, Kevin, et al. "On hyponormal operators in Krein spaces." Archivum Mathematicum 055.4 (2019): 249-259. <http://eudml.org/doc/294398>.
@article{Esmeral2019,
abstract = {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 $T$.},
author = {Esmeral, Kevin, Ferrer, Osmin, Jalk, Jorge, Lora Castro, Boris},
journal = {Archivum Mathematicum},
keywords = {Hyponormal operators; Krein spaces; $J$-hyponormal operators},
language = {eng},
number = {4},
pages = {249-259},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On hyponormal operators in Krein spaces},
url = {http://eudml.org/doc/294398},
volume = {055},
year = {2019},
}
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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 4
SP - 249
EP - 259
AB - 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 $T$.
LA - eng
KW - Hyponormal operators; Krein spaces; $J$-hyponormal operators
UR - http://eudml.org/doc/294398
ER -
References
top- Andô, T., 10.2307/2034629, Proc. Amer. Math. Soc. 14 (1963), 290–291. (1963) MR0145353DOI10.2307/2034629
- Azizov, T.Ya., Iokhvidov, I.S., Linear operator in spaces with an indefinite metric, Pure and Applied Mathematics, John Wiley Sons, 1989. (1989) MR1033489
- Berberian, S.K., Introduction to Hilbert space, Oxford University Press, 1961. (1961) MR0137976
- Bognar, J., Indefinite inner product spaces, Springer, 1974. (1974) MR0467261
- 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. (2009) MR2578108
- Cowen, C.C., Shaokuan, L., Hilbert space operators that are subnormal in the Krein space sense, J. Operator Theory 20 (1988), 165–181. (1988) MR0972187
- Esmeral, K., Ferrer, O., Castro, B. Lora, 10.12988/ijma.2016.6469, Int. J. Math. Anal. 19 (2016), 939–952. (2016) DOI10.12988/ijma.2016.6469
- Halmos, P.R., Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125–134. (1950) MR0044036
- McEnnis, B.W., Fundamental reducibility of selfadjoint operators on Krein space, J. Operator Theory 8 (1982), 219–225. (1982) MR0677413
- Putnam, C.R., 10.2140/pjm.1957.7.1649, Pacific J. Math. 7 (1957), 1649–1652. (1957) MR0093710DOI10.2140/pjm.1957.7.1649
- Sheth, I.H., 10.1090/S0002-9939-1966-0196498-7, Proc. Amer. Math. Soc. 17 (1966), 998–1000. (1966) MR0196498DOI10.1090/S0002-9939-1966-0196498-7
- Stampfli, J.G., 10.2140/pjm.1962.12.1453, Pacific J. Math. 12 (1962), 1453–1458. (1962) MR0149282DOI10.2140/pjm.1962.12.1453
- Xia, D., Spectral theory of hyponormal operators, Birkhäuser Verlag, 1983. (1983) MR0806959
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