A class of convolution algebras on compact fuzzy semigroups. (English) Zbl 0654.43001
The concept of a topological fuzzy semigroup S is introduced as a completely ordered set that is compact in the interval topology. It is proved that the set of all semicharacters of S constitutes a semigroup.
Starting from the linear space \(\bar C(S)\) of all continuous complex linear functionals on the linear space C(S) of all complex continuous mappings on S, the convolution semigroup M(S) of all measures corresponding to the elements of \(\bar C(S)\) is constructed, whose existence is guaranteed by means of the Riesz representation theorem. The remaining results of this paper concern the identification of the maximal ideals in the space \(\bar C(S)\) and the statement that \(\bar C(S)\) being a semisimple Banach algebra.
Starting from the linear space \(\bar C(S)\) of all continuous complex linear functionals on the linear space C(S) of all complex continuous mappings on S, the convolution semigroup M(S) of all measures corresponding to the elements of \(\bar C(S)\) is constructed, whose existence is guaranteed by means of the Riesz representation theorem. The remaining results of this paper concern the identification of the maximal ideals in the space \(\bar C(S)\) and the statement that \(\bar C(S)\) being a semisimple Banach algebra.
Reviewer: E.Kerre
Keywords:
topological fuzzy semigroup; completely ordered set; interval topology; semicharacters; complex linear functionals; convolution semigroup; measures; Riesz representation theoremReferences:
| [1] | Duchon, M., Structure theory for a class of convolution algebras of vector valued measures, Math. Nachr., 60, 97-108 (1974) · Zbl 0296.46046 |
| [2] | Hewitt, E.; Zuckerman, H. S., Structure theory for a class of convolution algebras, Pacific J. Math., 7-1, 913-941 (1957) · Zbl 0085.10002 |
| [3] | Kelley, J. L., General Topology (1955), Van Nostrand: Van Nostrand New York · Zbl 0066.16604 |
| [4] | Kim, Jin Bai, A certain matrix semigroup, Math. Japonica, 519-522 (1978) · Zbl 0383.22003 |
| [5] | Kim, Jin Bai, Note on the semigroup of fuzzy matrices, J. Korean Math. Soc., 16-1, 1-7 (1979) · Zbl 0417.20057 |
| [6] | Kim, Jin Bai, A note about inverses of Boolean matrices, Institute of Mathematics, Academia Sinica, 13-5, 231-235 (1985) · Zbl 0605.15011 |
| [7] | Preparata, F. P.; Yeh, R. T., Continuously valued logic, J. Comput. System Sci., 6-5, 397-418 (1972) · Zbl 0262.02020 |
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