Orapin WootijiruttikalS. C. OngP. ChaisuriyaJ. RakbudMahidol UniversityCentral Michigan UniversitySilpakorn University2018-09-132018-09-132009-01-01Operators and Matrices. Vol.3, No.3 (2009), 373-396184638862-s2.0-79955367653https://repository.li.mahidol.ac.th/handle/20.500.14594/27786Let A be a C* -algebra with identity 1; and let s(A) denote the set of all states on A. The state space s(A) (with the weak* topology) is used to construct classes of Banach spaces of functions defined on a fixed set S taking values in A. The inter-relationship between spaces are considered. Special classes of operators on these spaces are also considered. When A is taken to be C and S to be N, all spaces are just the classical spaces.Mahidol UniversityMathematicsArticleSCOPUS10.7153/oam-03-22