• Korean Journal of Mathematics
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• v.24 no.1
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• pp.65-70
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• 2016

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.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1207-1214
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• 2008

We give an elementary proof of one of the main results in [H.O. Kim, R.Y. Kim, J.K. Lim, The infimum cosine angle between two finitely generated shift-invariant spaces and its applications, Appl. Comput. Har-mon. Anal. 19 (2005) 253-281] concerning the existence of an oblique projection onto a finitely generated shift-invariant space along the orthogonal complement of another finitely generated shift-invariant space under the assumption that the generators generate Riesz bases.