Abstract. We prove several results concerning the representation of projections on arbitrary Banach spaces. We also give illustrative examples including an example of a generalized bi-circular projection which can not be written as the average of the identity with an isometric reflection. We also characterize generalized bi-circular projections on $C_0(\Omega,X)$, with $\Omega$ a locally compact Hausdorff space (not necessarily connected) and $X$ a Banach space with trivial centralizer.

DOI: 10.14232/actasm-012-060-2

AMS Subject Classification (1991): 47B38; 47B15, 46B99, 47A65

Keyword(s): generalized bi-circular projections, projections as combination of finite order operators, reflections, isometric reflections, isometries

Received August 10, 2012, and in revised form October 10, 2012. (Registered under 60/2012.)