Automorphisms and derivations of a Fréchet algebra of locally integrable functions

• Autorzy: F. Ghahramani , J. P. McClure
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46J45: Radical Banach algebras
• 43A20: L 1 -algebras on groups, semigroups, etc.
• 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 1
• Strony: 51-69

Daty

wydano

1992

otrzymano

1991-08-16

Twórcy

autor

F. Ghahramani

• Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

autor

J. P. McClure

• epartment of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

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