8 Banach C̃ - algebras
نویسنده
چکیده
We study Banach C̃-algebras, i.e., complete ultra-pseudo-normed algebras over the ring C̃ of Colombeau generalized complex numbers. We develop a spectral theory in such algebras. We show by explicit examples that important parts of classical Banach algebra theory do not hold for general Banach C̃algebras and indicate a particular class of Banach C̃-algebras that overcomes these limitations to a large extent. We also investigate C∗-algebras over C̃.
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