Automorphisms and derivations of a Fréchet algebra of locally integrable functions
Studia Mathematica, Tome 103 (1992) no. 1, pp. 51-69
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_sm_103_1_51_69,
author = {F. Ghahramani},
title = {Automorphisms and derivations of a {Fr\'echet} algebra of locally integrable functions},
journal = {Studia Mathematica},
pages = {51--69},
publisher = {mathdoc},
volume = {103},
number = {1},
year = {1992},
doi = {10.4064/sm-103-1-51-69},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-103-1-51-69/}
}
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%0 Journal Article %A F. Ghahramani %T Automorphisms and derivations of a Fréchet algebra of locally integrable functions %J Studia Mathematica %D 1992 %P 51-69 %V 103 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-103-1-51-69/ %R 10.4064/sm-103-1-51-69 %G en %F 10_4064_sm_103_1_51_69
F. Ghahramani. Automorphisms and derivations of a Fréchet algebra of locally integrable functions. Studia Mathematica, Tome 103 (1992) no. 1, pp. 51-69. doi: 10.4064/sm-103-1-51-69
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