Address:
Department of Mathematics, Universidad de Caldas, Calle 65 No. 26-10, Manizales, Colombia
Department of Mathematics, Universidad de Sucre, Carrera 28 No. 5 –267 Barrio Puerta Roja, Sincelejo, Colombia
Department of Mathematics, Universidad del Atlántico, Km 7 Antigua vía Puerto Colombia, Barranquilla, Colombia
E-mail:
kevin.esmeral@ucaldas.edu.co
osmin.ferrer@unisucre.edu.co
jjalkpta@gmail.com
borisjose62@gmail.com
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 $T$.
AMSclassification: primary 47B50; secondary 46C20.
Keywords: Hyponormal operators, Krein spaces, J-hyponormal operators.
DOI: 10.5817/AM2019-4-249