Abstract. In this note we discuss the Taylor--Weyl spectrum of a commuting pair of operators acting on a Hilbert space and compare the Taylor--Weyl spectrum with a joint Weyl spectrum due to Chō and Takaguchi.

AMS Subject Classification (1991): 47A13, 47A10, 47A53

Received December 20, 1993 and in revised form March 25, 1994. (Registered under 5581/2009.)