On Fredholm Operators Between Non-archimedean Fréchet Spaces
Copyright policy )On Fredholm Operators Between Non-archimedean Fréchet Spaces
Although compact perturbations of operators on non-Archimedean Banach spaces have long been studied by a number of authors, it was proved in full generality only recently that the index of a Fredholm operator between non-Archimedean Banach spaces is preserved under compact perturbations [\textit{J. Araujo}, \textit{C. Perez-Garcia} and \textit{S. Vega}, Compos. Math. 118, 291--303 (1999; Zbl 1038.47047)]. In the paper under review, this result is extended to operators between non-archimedean Fréchet spaces and also to the case of a Fredholm operator from a polar regular LF-space to an LF-space (the inductive limit of an inductive sequence of non-Archimedean Fréchet spaces).
Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, non-archimedean Fréchet space, Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory, (Semi-) Fredholm operators; index theories, Fredholm operator, compact perturbation, LF-space
Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, non-archimedean Fréchet space, Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory, (Semi-) Fredholm operators; index theories, Fredholm operator, compact perturbation, LF-space
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