Abstract. In paper [5] B. Sz.-Nagy proved his famous theorem about contractions in complex Hilbert spaces. In this paper we generalize his theorem to quaternion Hilbert spaces.

AMS Subject Classification (1991): 47A10

Keyword(s): Quaternion Hilbert spaces, operator, spectrum, contractions

Received July 11, 2006, and in revised form October 4, 2006. (Registered under 5966/2009.)