ACTA issues

Riesz operators and Schur's lemma

Béla Nagy

Acta Sci. Math. (Szeged) 80:3-4(2014), 639-650

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.)