Abstract.
Let be a C* -algebra. Let f be a non-constant complex-valued continuous function defined on a closed interval I. We shall show that f densely spans As an application, is commutative if f(x)f(y)=f(y)f(x) for all self-adjoint elements x and y in with spectrums contained in I.
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Acknowledgments.
We would like to express our deep gratitude to Professor Lawrence G. Brown for several useful advices.
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Mathematics Subject Classification (1991):Primary 46L05
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Jeang, JS., Ko, CC. On the commutativity of C* -algebras. manuscripta math. 115, 195–198 (2004). https://doi.org/10.1007/s00229-004-0488-3
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DOI: https://doi.org/10.1007/s00229-004-0488-3