Automorphisms and derivations of a Fréchet algebra of locally integrable functions

Ghahramani, F. ; McClure, J.

Studia Mathematica, Tome 103 (1992), p. 51-69 / Harvested from The Polish Digital Mathematics Library

Résumé

We find representations for the automorphisms, derivations and multipliers of the Fréchet algebra $L¹_{loc}$ of locally integrable functions on the half-line $ℝ^+$. We show, among other things, that every automorphism θ of $L¹_{loc}$ is of the form $θ = φ _ae^{λX}e^D$, 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 $(φ_af)(x) = af(ax)$ ($f ∈ L¹_{loc}$, $x ∈ ℝ^+$). It is also shown that the automorphism group is a topological group with the topology of uniform convergence on bounded sets and is the semidirect product of a connected subgroup and a discrete group which is isomorphic to the discrete group of real numbers.

Détail

Publié le : 1992-01-01

Zbl 0813.46043

EUDML-ID : urn:eudml:doc:215935

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