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.
AMS Subject Classification
(1991): 47B06, 47B40; 15A21
resolutionof the identity
Received October 10, 2012. (Registered under 92/2012.)