Korean J. Math. Vol. 24 No. 1 (2016) pp.65-70
DOI: https://doi.org/10.11568/kjm.2016.24.1.65

Riesz projections for a non-hyponormal operator

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Published: Mar 30, 2016
Keywords:
Riesz projections, ($G_1$) property
Mathematics Subject Classification:
47A10, 47B20.

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Jae Won Lee
Department of Applied Mathematics Kumoh National Institute of Technology Gumi 730-701Korea
In Ho Jeon
Department of Mathematics Education Seoul National University of Education Seoul 137-742 Korea

Abstract

J. G. Stampfli proved that if a bounded linear operator $T$ on a Hilbert space $\mathscr H$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with $\lambda\in{\rm iso}\sigma(T)$ is self-adjoint and $P_{\lambda}\mathscr{H}=(T - \lambda)^{-1}(0)=(T^{*} - \bar{\lambda})^{-1}(0)$.
In this note we show that Stampfli's result is generalized to an nilpotent extension of an operator having ($G_1$) property.



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