When are full representations of algebras of operators on Banach spaces automatically faithful?

@article{Horvath2018WhenAF,
  title={When are full representations of algebras of operators on Banach spaces automatically faithful?},
  author={Bence Horv'ath},
  journal={arXiv: Functional Analysis},
  year={2018}
}
We examine the phenomenon when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we shall show that for certain Banach spaces $X$ the following property holds: For every non-zero Banach space $Y$ every surjective algebra homomorphism $\psi: \, \mathcal{B}(X) \rightarrow \mathcal{B}(Y)$ is automatically injective. In the second part of the paper we consider the question in the opposite direction: Building… Expand
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