Search results for "unital"
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Locally Convex Quasi C*-Algebras and Their Structure
2020
Throughout this chapter \({{\mathfrak A}}_{\scriptscriptstyle 0}[\| \cdot \|{ }_{\scriptscriptstyle 0}]\) denotes a unital C*-algebra and τ a locally convex topology on \({{\mathfrak A}}_{\scriptscriptstyle 0}\). Let \(\widetilde {{{\mathfrak A}}_{\scriptscriptstyle 0}}[\tau ]\) denote the completion of \({{\mathfrak A}}_{\scriptscriptstyle 0}\) with respect to the topology τ. Under certain conditions on τ, a subspace \({\mathfrak A}\) of \(\widetilde {{{\mathfrak A}}_{\scriptscriptstyle 0}}[\tau ]\), containing \({{\mathfrak A}}_{\scriptscriptstyle 0}\), will form (together with \({{\mathfrak A}}_{\scriptscriptstyle 0}\)) a locally convex quasi *-algebra \(({\mathfrak A}[\tau ],{{\mathfrak…
A NOTE ON THE CATEGORICAL NOTIONS OF NORMAL SUBOBJECT AND OF EQUIVALENCE CLASS
2021
In a non-pointed category E, a subobject which is normal to an equivalence relation is not necessarily an equivalence class. We elaborate this categorical distinction, with a special attention to the Mal'tsev context. Moreover, we introduce the notion of fibrant equipment, and we use it to establish some conditions ensuring the uniqueness of an equivalence relation to which a given subobject is normal, and to give a description of such a relation.