Abstract. We determine when the average of two isometries on a Banach space of analytic vector valued functions is a projection. We also characterize the generalized bi-circular projections on a Banach space of absolutely continuous vector valued functions.

DOI: 10.14232/actasm-013-781-8

AMS Subject Classification (1991): 30D05

Keyword(s): bi-circular projections, Hardy spaces, isometry, convex combination of isometries

Received May 21, 2013, and in revised form February 14, 2014. (Registered under 31/2013.)