The connectedness of the group of automorphisms of

Author:
F. Ghahramani

Journal:
Trans. Amer. Math. Soc. **302** (1987), 647-659

MSC:
Primary 46J35; Secondary 43A20

DOI:
https://doi.org/10.1090/S0002-9947-1987-0891639-6

MathSciNet review:
891639

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Abstract: For each of the radical Banach algebras and an integral representation for the automorphisms is given. This is used to show that the groups of the automorphisms of and endowed with bounded strong operator topology (BSO) are arcwise connected. Also it is shown that if denotes the norm of , , , then the group of automorphisms of topologized by is arcwise connected. It is shown that every automorphism of is of the form , where each is a quasinilpotent derivation. It is shown that the group of principal automorphisms of under operator norm topology is arcwise connected, and every automorphism has the form , where , , and is a derivation, and where denotes the extension by continuity of from a dense subalgebra of to .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0891639-6

Keywords:
Automorphism,
derivation,
connectedness,
quasinilpotent derivation

Article copyright:
© Copyright 1987
American Mathematical Society