1University of Los Andes, Mérida, Venezuela. Email: barcenas@ula.ve
2University of Los Andes, Mérida, Venezuela. Email: walterespinoza@hotmail.com
3University of Los Andes, Mérida, Venezuela. Email: edixonr@ula.ve
]]>
It is proved in this paper that several classical Banach algebras are not isomorphic to a group algebra. These algebras includes C(K) algebras where K is a compact Hausdorff space. In the case of amalgams, we give conditions for an amalgam to be a group algebra.
Key words: Amalgams, Dunford-Pettis property, Radon-Nikodym property.
En este artículo se prueba que algunas álgebras de Banach clásicas no son isomorfas a un álgebra de grupo. Estas álgebras incluyen a las álgebras C(K) donde K es un espacio de Hausdorff Compacto. En el caso de las amalgamas, damos condiciones para que una amalgama sea un álgebra de grupo.
Palabras clave: Amalgamas, propiedad de Dunford-Pettis, propiedad de Radon-Nikodym.
Texto completo disponible en PDF
[1] Bachman, G., Elements of Abstract Harmonic Analysis, Academic Press, New York, United States, 1964. [ Links ]
[2] Bertrandias, J., Datry, C. & Dupuis, C., `Union et intersections d' espaces Lp invariantes par traslation ou convolution´, Ann. Inst. Fourier 28, 2 (1978), 53-84. [ Links ]
[3] Bottcher, A., Karlovich, Y. & Spitkovsky, I., Convolution Operator and Factorization of Almost Periodic Matrix Functions, Birkhauser, Basel, Germany, 2002. [ Links ]
[4] Carother, N., A short Course on Banach Spaces Theory, Cambridge University Press, Cambridge, United States, 2005. [ Links ]
[5] Conway, J., A Course in Functional Analysis, Springer Verlag, New York, United States, 1990. [ Links ]
[6] Conway, J., A Course in Operator Theory, Vol. 21 of GMS, AMS, Providence, United States, 2000. [ Links ]
[7] Delbaen, F., `Weakly compact operators on the disk algebra´, Journal of Algebra 45, (1977), 284-294. [ Links ]
[8] Diestel, J., `A survey of results related the Dunford Pettis property´, Contemporary Math. 2, (1980), 15-60. [ Links ]
[9] Diestel, J., Sequences and Series in Banach Spaces, Springer Verlag, Berlin, Germany, 1984. [ Links ]
[10] Diestel, J. & Uhl, J., Vector Measures, Vol. 15 of Math. Surveys, Amer. Math. Soc., Providence, United States, 1977. [ Links ]
[11] Dunford, N. & Schwartz, J., Linear Operator. Part I: General Theory, Wiley Intercience, New York, United States, 1957. [ Links ]
[12] Goldberg, R., `On a space of functions of Wiener´, Duke Math. 34, 5 (1967), 683-691. [ Links ]
[13] Holland, F., `Harmonic analysis on amalgams of Lp and lq´, J. London Math. Soc. 10, 2 (1975), 195-305. [ Links ]
[14] Stewart, J. & Watson, S., `Which amalgams are convolution algebras?´, Proc. Amer. Math. Soc. 93, 4 (1985), 621-627. [ Links ]
[15] Wojtaszcyk, P., Banach Spaces for Analyst, Cambridge University Press, Cambridge, United States, 1991. [ Links ]
[16] Zelasco, W., `On the algebras Lp of locally compact groups´, Colloq. Math. 8, (1961), 115-120. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv42n1a06,
AUTHOR = {Barcenas, Diomedes and Espinoza, Walter and Rojas, Edixon}, ]]>
TITLE = {{A note on Banach algebras that are not isomorphic to a group algebra}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2008},
volume = {42},
number = {1},
pages = {67-72}
}