Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K)

Malahayati Malahayati


The first Baire class of bounded functions on separable metric spaces K denoted by B1(k). One of the most important subclass of B1(k) is D(K), by D(K) is denoted the class of all functions on K which are differences of bounded semicontinuous functions. In this paper we proved that D(K) is abelian Banach algebra and identity element


Separable metric spaces; Banach Algebra; The first Baire class; Semicontinuous functions; The Class D(K)

Full Text:



Ash, R.B., 2007, Real Variables with Basic Metric Space Topology, Department of Mathematics University of Illionis at Urbana-Champaign.

Dugundji, J., 1966, Topology, Allyn and Bacon, Inc., Boston.

Farmaki, V., 1996, On Baire-14⁄ Functions, Trans. Amer. Math. Soc, 348, 10.

Gordon, R.A., 1994, The Integral of Lebesgue, Denjoy, Perron and Henstock, American Mathematical Society, USA.

Haydon, R., Odell, E. dan Rosenthal, H.P., 1991, On Certain Classes of Baire-1 Functions with Applications to Banach Space Theory, Lecture Notes in Math., 1470, Springer, New York.

Kreyszig, E., 1978, Introductory Functional Analysis with Applications, John Wiley and Sons, Inc., Canada.

McShane, E.J., 1944, Integration, Princeton University Press, Princeton.

Rosenthal, H.P., 1994, A Characterization of Banach Spaces Containing C0, J. Amer. Math. Soc, 7, 3, 707-748.

Rosenthal, H.P., 1994, Differences of Bounded Semi-Continuous Functions I,, 20 Juni 1994,

Royden, H.L., 1989, Real Analysis, Macmillan Publishing Company, New York



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.