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Composition operators on spaces of real analytic functions

✍ Scribed by Paweł Domański; Michael Langenbruch

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
259 KB
Volume
254-255
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let Ω1, Ω2 be open subsets of R d 1 and R d 2 , respectively, and let A(Ω1) denote the space of real analytic functions on Ω1. We prove a Glaeser type theorem by characterizing when a composition operator Cϕ :

Using this result we characterize when A(Ω1) can be embedded topologically into A(Ω2) as a locally convex space or as a topological algebra. We also characterize LB-subspaces and Fréchet subspaces of A(Ω1). In particular, it follows that if A(Ω1) and A(Ω2) are isomorphic as locally convex spaces, then d1 = d2.

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