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Automorphisms and derivations of a Fréchet algebra of locally integrable functions

100%

Ghahramani F., McClure J. P.

Studia Mathematica

1992

tom 103

nr 1

51-69

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.

Pseudo-Banach algebras

50%

Allan G. R., Dales H. G., McClure J. P.

Studia Mathematica

1971

tom 40

nr 1

55-69

Ograniczanie wyników

2 Studia Mathematica

2 McClure J. P.

1 Allan G. R.

1 Dales H. G.

1 Ghahramani F.

1 1992

1 1971

Wyniki wyszukiwania

Automorphisms and derivations of a Fréchet algebra of locally integrable functions

Pseudo-Banach algebras