Year: 2008
Type: preprint
Abstract: We study Banach $\widetilde{\mathbb C}$-algebras, i.e., complete ultra-pseudo-normed algebras over the ring $\widetilde{\mathbb C}$ 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 $\widetilde{\mathbb C}$-algebras and indicate a particular class of Banach $\widetilde{\mathbb C}$-algebras that overcomes these limitations to a large extent. We also investigate C*-algebras over $\widetilde{\mathbb C}$.
Source: arXiv (Cornell University)
Author: Vernaeve, Hans
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1537831564