Fix a permitted carrier class and morphism class before testing a context. A realization of is a dense-image linear map , , and operators with and for every . Such contexts form .
Meaning and scope
Admissibility is relative to these declared carriers, topologies, domains, and allowed maps. It does not simply mean that an algebraic formula exists.
Example
Coordinate projection is bounded on Euclidean space. Coordinate summation on is algebraically defined but is not closable in its usual source realization.
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