Two classes of $J$-operators

Document Type : Dedicated to Prof. A. T.-M. Lau

Author

Hokkaido University (Emeritus), Sapporo, Japan

Abstract

We define two classes ${\mathfrak A}$ and ${\mathfrak B}$ in the space ${\mathcal B}({\mathcal H})$ of operators acting on a Hilbert space on the basis of $J$-order relation and spectra, and discuss various properties related to these classes.

Keywords

Main Subjects


Ando, Linear Operators on Kreĭn Spaces, Hokkaido University, Research Institute of Applied Electricity, Division of Applied Mathematics, Sapporo, 1979.
Ando, Löwner inequality of indefinite type, Linear Algebra Appl. 385 (2004) 73--80.
Ya. Azizov and I. S. Iokhvidov, Linear Operators in Spaces with an Indefinite Metric, Nauka, Moscow, 1986, English translation: Wiley, New York, 1989.
Gohberg, P. Lancaster and L. Rodman, Indefinite linear algebra and applications, Birkhäuser Verlag, Basel, 2005.
Hassi and K. Nordström, Antitonicity of the inverse and J-contractivity, Gheondea, A. (ed.) et al., Operator extensions, interpolation of functions and related topics. 14th international conference on operator theory, Timisoara (Romania), June 1-5, 1992. Basel, Birkhäuser Verlag. Oper. Theory, Adv. Appl. 61 (1993), 149--161.
Sano, Furuta inequality of indefinite type, Math. Inequal. Appl. 10 (2007), no. 2, 381--387.