  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. Frechet algebras of holomorphic functions. 7. Spaces of
continuous functions.
