Author/Editor		Drnovšek, Roman; Livshits, Leo; MacDonald, Gordon; Mathes, Ben; Radjavi, Heydar; Šemrl, Peter
Title		On operator bands
Type		članek
Source		Stud Math
Vol. and No.		Letnik 139, št. 1
Publication year		2000
Volume		str. 91-100
Language		eng
Abstract		A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K > 1 there exists an irreducible operator band on the Hilbert space l2 which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each member has operator norm equal to 1. Given a positive integer r, we introduce a notion of weak r-transitivity of a set of bounded operators on a Banach space. We construct an operator band on l2 that is weakly r-transitive and is not weakly (r + 1)-transitive. We also study operator bands S satisfying a polynomial identity p(A, B) = 0 for all non-zero A, B E S, where p is a given polynomial in two non-commuting variables. It turns out that the polynomial p(A, B) = (AB - BA)2 has a special role in these considerations.
Descriptors		MATHEMATICS MODELS, THEORETICAL