Abstract. A new method for constructing irreducible operator bands is provided. Using this, we are able to answer some open problems concerning bands. In particular, there exists a non-negative irreducible operator band.

AMS Subject Classification (1991): 47A15, 47D03, 15A30

Keyword(s): operator semigroups, idempotents, band, reducible, non-negative

Received February 2, 2000, and in revised form July 6, 2000. (Registered under 2786/2009.)