Stability of the surjectivity of endomorphisms and isometries of ℬ(ℋ)

Molnár, Lajos

doi:10.1090/S0002-9939-98-04130-6

Stability of the surjectivity of endomorphisms and isometries of $\mathcal {B}(H)$
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Proc. Amer. Math. Soc. 126 (1998), 853-861 Request permission

Abstract:

We determine the largest positive number $c$ with the property that whenever $\Phi ,\Psi$ are endomorphisms, respectively unital isometries of the algebra of all bounded linear operators acting on a separable Hilbert space, $\| \Phi (A)-\Psi (A)\|<c\| A\|$ holds for every nonzero $A$ and $\Phi$ is surjective, then so is $\Psi$. It turns out that in the first case we have $c=1$, while in the second one $c=2$.

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