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

Malahayati Malahayati

Abstract


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

Keywords


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

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References


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, http://www.arxiv.org/abs/math/9406217, 20 Juni 1994,

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




DOI: https://doi.org/10.18860/ca.v3i1.3112

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