# Automorphisms and derivations of a Fréchet algebra of locally integrable functions

Studia Mathematica (1992)

- Volume: 103, Issue: 1, page 51-69
- ISSN: 0039-3223

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topGhahramani, F., and McClure, J.. "Automorphisms and derivations of a Fréchet algebra of locally integrable functions." Studia Mathematica 103.1 (1992): 51-69. <http://eudml.org/doc/215935>.

@article{Ghahramani1992,

abstract = {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.},

author = {Ghahramani, F., McClure, J.},

journal = {Studia Mathematica},

keywords = {representations; automorphisms; derivations; multipliers; Fréchet algebra; locally integrable functions on the half-line; dilation operator; automorphism group; topology of uniform convergence on bounded sets; semidirect product of a connected subgroup and a discrete group},

language = {eng},

number = {1},

pages = {51-69},

title = {Automorphisms and derivations of a Fréchet algebra of locally integrable functions},

url = {http://eudml.org/doc/215935},

volume = {103},

year = {1992},

}

TY - JOUR

AU - Ghahramani, F.

AU - McClure, J.

TI - Automorphisms and derivations of a Fréchet algebra of locally integrable functions

JO - Studia Mathematica

PY - 1992

VL - 103

IS - 1

SP - 51

EP - 69

AB - 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.

LA - eng

KW - representations; automorphisms; derivations; multipliers; Fréchet algebra; locally integrable functions on the half-line; dilation operator; automorphism group; topology of uniform convergence on bounded sets; semidirect product of a connected subgroup and a discrete group

UR - http://eudml.org/doc/215935

ER -

## References

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