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http://dx.doi.org/10.11568/kjm.2016.24.1.65

RIESZ PROJECTIONS FOR A NON-HYPONORMAL OPERATOR  

Lee, Jae Won (Department of Applied Mathematics Kumoh National Institute of Technology)
Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
Publication Information
Korean Journal of Mathematics / v.24, no.1, 2016 , pp. 65-70 More about this Journal
Abstract
J. G. Stampfli proved that if a bounded linear operator T on a Hilbert space ${\mathfrak{H}}$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with ${\lambda}{\in}iso{\sigma}$(T) is self-adjoint and $P_{\lambda}{\mathfrak{H}}=(T-{\lambda})^{-1}(0)=(T^*-{\bar{\lambda}})^{-1}(0)$. In this note we show that Stampfli''s result is generalized to an nilpotent extension of an operator having ($G_1$) property.
Keywords
Riesz projections; ($G_1$) property;
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