Abstract
We investigate the reflexivity of the isometry group and the automorphism group of some important metric linear spaces and algebras. The paper consists of the following sections: 1) Preliminaries. 2) Sequence spaces. 3) Spaces of measurable functions. 4) Hardy spaces. 5) Banach algebras of holomorphic functions. 6) Fréchet algebras of holomorphic functions. 7) Spaces of continuous functions.
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