TL;DR
This paper explores classes of linear operators on Banach spaces over non-Archimedean fields that allow for orthogonal spectral decompositions, providing theoretical insights and concrete examples.
Contribution
It introduces new classes of normal operators in non-Archimedean Banach spaces with spectral decomposition properties, expanding the understanding of operator theory in this setting.
Findings
Identification of classes of normal operators with spectral decompositions
Provision of concrete examples illustrating these classes
Advancement of spectral theory in non-Archimedean analysis
Abstract
We describe some classes of linear operators on Banach spaces over non-Archimedean fields, which admit orthogonal spectral decompositions. Several examples are given.
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