Vol. 46, No. 2, 1973

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Starlike and convex maps in Banach spaces

Ted Joe Suffridge

Vol. 46 (1973), No. 2, 575–589
Abstract

Let X and Y be complex Banach spaces and let B = {x X : x< 1}. This paper concerns holomorphic maps f : B Y which have local holomorphic inverses. That is, for each x B, there is a neighborhood N Y of f(x) and a holomorphic function g : N B such that g(f(x)) = x and f(g(y)) = y for all y N. Necessary and sufficient conditions are found which guarantee that such a map be one-to-one and map the unit ball B onto a domain which is convex or starlike with respect to 0.

Mathematical Subject Classification 2000
Primary: 46G20
Milestones
Received: 27 March 1972
Published: 1 June 1973
Authors
Ted Joe Suffridge