Quasirepresentations and pseudorepresentations (Q1814370)

Let \(E\) be a locally convex topological vector space, \(\mathcal P\) be a family of seminorms on \(E\) generating its topology, \(L(E)\) be the algebra of continuous, linear operators on \(E\), \(S\) be a semigroup, and \(\varepsilon>0\). A map \(T:S\to L(E)\) is called an \(\varepsilon\)- quasirepresentation if \(p(T(hg)x-T(h)T(g))\leq\varepsilon p(x)\) for all \(h,g\in S\), \(x\in E\), and \(p\in\mathcal P\). The author studies relations between quasirepresentations and representations, related notions, particular cases, and examples.