Abstract
We describe a method of extending certain stability results valid for real-valued functions to the class of functions with range in an f-algebra. The method is based on the Spectral Representation Theory for Riesz spaces. Details will be presented for the multiplicative Dhombres functional equation
In this note we use the Ogasawara–Maeda Spectral Representation Theorem for Riesz spaces which will be firstly adapted to the f-algebras reality.
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Batko, B. Spectral representation theory and stability of the multiplicative Dhombres functional equation in f-algebras. Aequat. Math. 89, 543–554 (2015). https://doi.org/10.1007/s00010-013-0234-6
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DOI: https://doi.org/10.1007/s00010-013-0234-6