Abstract. We characterize the generalized bi-circular projections on various Banach spaces of both scalar and vector valued analytic functions, including the Bergman, Bloch, and Hardy spaces. We also establish that the only projections in the convex hull of two isometries on a Hardy space are generalized bi-circular projection.

AMS Subject Classification (1991): 30D55; 30D05

Keyword(s): isometry, convex combination of isometries

Received July 16, 2008, and in revised form September 10, 2008. (Registered under 6427/2009.)