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Automorphisms and derivations of a Fréchet algebra of locally integrable functions

F. GhahramaniJ. McClure — 1992

Studia Mathematica

We find representations for the automorphisms, derivations and multipliers of the Fréchet algebra L ¹ l o c of locally integrable functions on the half-line + . We show, among other things, that every automorphism θ of L ¹ l o c is of the form θ = φ a e λ X e D , where D is a derivation, X is the operator of multiplication by coordinate, λ is a complex number, a > 0, and φ a is the dilation operator ( φ a f ) ( x ) = a f ( a x ) ( f L ¹ l o c , x + ). It is also shown that the automorphism group is a topological group with the topology of uniform convergence on bounded...

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