Representations of Banach algebras subordinate to topologically introverted spaces

@article{Filali2015RepresentationsOB,
  title={Representations of Banach algebras subordinate to topologically introverted spaces},
  author={Mahmoud Filali and Matthias Neufang and Mehdi Sangani Monfared},
  journal={Transactions of the American Mathematical Society},
  year={2015},
  volume={367},
  pages={8033-8050}
}
Let A be a Banach algebra, X a closed subspace of A∗, Y a dual Banach space with predual Y∗, and π a continuous representation of A on Y. We call π subordinate to X if each coordinate function πy,λ ∈ X, for all y ∈ Y, λ ∈ Y∗. If X is topologically left (right) introverted and Y is reflexive, we show the existence of a natural bijection between continuous representations of A on Y subordinate to X, and normal representations of X∗ on Y. We show that if A has a bounded approximate identity, then… 
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