# The order structure of the space of measures with continuous translation

Annales de l'institut Fourier (1982)

- Volume: 32, Issue: 2, page 67-110
- ISSN: 0373-0956

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topSleijpen, Gérard L. G.. "The order structure of the space of measures with continuous translation." Annales de l'institut Fourier 32.2 (1982): 67-110. <http://eudml.org/doc/74542>.

@article{Sleijpen1982,

abstract = {Let $G$ be a locally compact group, and let $\Vert ~~\Vert ^B_\infty $ be a function norm on $L^1(G)_\{\rm loc\}$ such that the space $L^\infty (G,B)$ of all locally integrable functions with finite $\Vert ~~\Vert ^B_\infty $-norm is an invariant solid Banach function space. Consider the space $L_\{\rm RUC\}(G,B)$ of all functions in $L^\infty (G,B)$ of which the right translation is a continuous map from $G$ into $L^\infty (G,B)$. Characterizations of the case where $L_\{\rm RUC\}(G,B)$ is a Riesz ideal of $L^\infty (G,B)$ are given in terms of the order-continuity of $\Vert ~~\Vert ^B_\infty $ on certain subspaces of $L^\infty (G)$. Throughout the paper, the discussion is carried out in the context of and all the results are formulated for foundation semigroups with identity element; any locally compact group is an example of such a semigroup.},

author = {Sleijpen, Gérard L. G.},

journal = {Annales de l'institut Fourier},

keywords = {Riesz ideal; function spaces with continuous translation},

language = {eng},

number = {2},

pages = {67-110},

publisher = {Association des Annales de l'Institut Fourier},

title = {The order structure of the space of measures with continuous translation},

url = {http://eudml.org/doc/74542},

volume = {32},

year = {1982},

}

TY - JOUR

AU - Sleijpen, Gérard L. G.

TI - The order structure of the space of measures with continuous translation

JO - Annales de l'institut Fourier

PY - 1982

PB - Association des Annales de l'Institut Fourier

VL - 32

IS - 2

SP - 67

EP - 110

AB - Let $G$ be a locally compact group, and let $\Vert ~~\Vert ^B_\infty $ be a function norm on $L^1(G)_{\rm loc}$ such that the space $L^\infty (G,B)$ of all locally integrable functions with finite $\Vert ~~\Vert ^B_\infty $-norm is an invariant solid Banach function space. Consider the space $L_{\rm RUC}(G,B)$ of all functions in $L^\infty (G,B)$ of which the right translation is a continuous map from $G$ into $L^\infty (G,B)$. Characterizations of the case where $L_{\rm RUC}(G,B)$ is a Riesz ideal of $L^\infty (G,B)$ are given in terms of the order-continuity of $\Vert ~~\Vert ^B_\infty $ on certain subspaces of $L^\infty (G)$. Throughout the paper, the discussion is carried out in the context of and all the results are formulated for foundation semigroups with identity element; any locally compact group is an example of such a semigroup.

LA - eng

KW - Riesz ideal; function spaces with continuous translation

UR - http://eudml.org/doc/74542

ER -

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