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A Schwarz Lemma for Convex Domains in Arbitrary Banach Spaces

✍ Scribed by Luis Bernal-González

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
133 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this note the following new version of the Schwarz lemma is proved: If f is a holomorphic function mapping a bounded convex domain D D of a complex Banach 1 Ž . space into a convex domain D D of another complex Banach space and f a s b, 2 then the image by f of the set of points in D D lying at a distance greater than r 1 from the frontier of D D is at a positive distance from the frontier of D D . This 1 2

distance depends only upon a, b, and r, and it can be estimated specifically in terms of the norms of the Banach spaces. Our result extends several earlier theorems.

📜 SIMILAR VOLUMES

A Bound for the Modulus of Continuity fo
A Bound for the Modulus of Continuity for Metric Projections in a Uniformly Convex and Uniformly Smooth Banach Space
✍ Ya.I. Alber 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 318 KB

In 1979, Bjornestal obtained a local estimate for a modulus of uniform continuity of the metric projection operator on a closed subspace in a uniformly convex and uniformly smooth Banach space B. In the present paper we give the global version of this result for the projection operator on an arbitra