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Abstract. We present sufficient conditions in order (the space of) a Riesz operator $T$ in a Hilbert space $H$ have a Jordan--Schur basis with respect to a scalar product equivalent to the original one. This is related to Schur's lemma for a compact operator, which is an extension of Schur's classical theorem on unitary triangularization in a finite dimensional space. The finite dimensional case is also studied.
DOI: 10.14232/actasm-012-092-8
AMS Subject Classification
(1991): 47B06, 47B40; 15A21
Keyword(s):
Riesz operator,
Schur's lemma,
unitary triangularization,
equivalent scalarproduct,
Jordan--Schurbasis,
spectraloperator,
resolutionof the identity
Received October 10, 2012. (Registered under 92/2012.)
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