Surjective Homomorphisms from Algebras of Operators on Long Sequence Spaces are Automatically Injective
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DOI: 10.1093/qmath/haaa066
Abstract: We study automatic injectivity of surjective algebra homomorphisms from $\mathscr{B}(X)$, the algebra of (bounded, linear) operators on $X$, to $\mathscr{B}(Y)$, where $X$ is one of the following \emph{long} sequence spaces: $c_0(\lambda)$, $\ell_{\infty}^c(\lambda)$, and $\ell_p(\lambda)$ ($1… read more here.
Keywords: long sequence; algebras operators; surjective homomorphisms; sequence spaces ... See more keywords