# Completely continuous multipliers from ${L}_{1}\left(G\right)$ into ${L}_{\infty}\left(G\right)$

Annales de l'institut Fourier (1984)

- Volume: 34, Issue: 2, page 137-154
- ISSN: 0373-0956

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topCrombez, G., and Govaerts, Willy. "Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$." Annales de l'institut Fourier 34.2 (1984): 137-154. <http://eudml.org/doc/74626>.

@article{Crombez1984,

abstract = {For a locally compact Hausdorff group $G$ we investigate what functions in $L_\infty (G)$ give rise to completely continuous multipliers $T_g$ from $L_1(G)$ into $L_\infty (G)$. In the case of a metrizable group we obtain a complete description of such functions. In particular, for $G$ compact all $g$ in $L_\infty (G)$ induce completely continuous $T_g$.},

author = {Crombez, G., Govaerts, Willy},

journal = {Annales de l'institut Fourier},

keywords = {completely continuous operator; L1(G); L-infinity (G); uniformly measurable functions; multiplier},

language = {eng},

number = {2},

pages = {137-154},

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

title = {Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$},

url = {http://eudml.org/doc/74626},

volume = {34},

year = {1984},

}

TY - JOUR

AU - Crombez, G.

AU - Govaerts, Willy

TI - Completely continuous multipliers from $L_1(G)$ into $L_\infty (G)$

JO - Annales de l'institut Fourier

PY - 1984

PB - Association des Annales de l'Institut Fourier

VL - 34

IS - 2

SP - 137

EP - 154

AB - For a locally compact Hausdorff group $G$ we investigate what functions in $L_\infty (G)$ give rise to completely continuous multipliers $T_g$ from $L_1(G)$ into $L_\infty (G)$. In the case of a metrizable group we obtain a complete description of such functions. In particular, for $G$ compact all $g$ in $L_\infty (G)$ induce completely continuous $T_g$.

LA - eng

KW - completely continuous operator; L1(G); L-infinity (G); uniformly measurable functions; multiplier

UR - http://eudml.org/doc/74626

ER -

## References

top- [1] G. CROMBEZ and W. GOVAERTS, Weakly compact convolution operators in L1(G), Simon Stevin, 52 (1978), 65-72. Zbl0379.43004MR80a:43008
- [2] G. CROMBEZ and W. GOVAERTS, Towards a classification of convolution-type operators from l1 to l∞, Canad. Math. Bull., 23 (1980), 413-419. Zbl0446.47017MR82f:47038
- [3] J. DIESTEL and J. J. UHL, Vector measures, Math. Surveys n° 15, Amer. Math. Soc., Providence, R.I., 1977. Zbl0369.46039MR56 #12216
- [4] N. DUNFORD and J. T. SCHWARTZ, Linear operators, part I, New-York, Interscience, 1958. Zbl0084.10402MR22 #8302
- [5] R. E. EDWARDS, Functional analysis, New-York, Holt, Rinehart and Winston, 1965. Zbl0182.16101MR36 #4308
- [6] R. HERMAN, Generalizations of weakly compact operators, Trans. Amer. Math. Soc., 132 (1968), 377-386. Zbl0159.43004MR36 #6976
- [7] E. HEWITT and K. A. ROSS, Abstract harmonic analysis, I, Berlin, Springer, 1963. Zbl0115.10603
- [8] A. PELCZYNSKI, On strictly singular and strictly cosingular operators, II, Bull. Acad. Polon. Sci., Sér. Sc. Math. Astronom. Phys., 13 (1965), 37-41. Zbl0138.38604MR31 #1564
- [9] A. PIETSCH, Operator ideals, Amsterdam, North-Holland Publ. Comp., 1980. Zbl0434.47030MR81j:47001
- [10] K. YLINEN, Characterizations of B(G) and B(G)∩AP(G) for locally compact groups, Proc. Amer. Math. Soc., 58 (1976), 151-157. Zbl0333.43004MR54 #13472

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