论文标题
运营商代数在Banach空间的代数之间的溢出性同态扰动
Perturbations of surjective homomorphisms between algebras of operators on Banach spaces
论文作者
论文摘要
Molnár的显着结果[Proc。阿米尔。数学。 Soc。，126（1998），853-861]指出，在“小”扰动下，作用于可分离的希尔伯特空间的操作员代数的自动形态是稳定的。更确切地说，如果$ ϕ，ψ$是$ \ Mathcal {b}（\ Mathcal {h}）$的内态性，以至于$ \ | ϕ（a） - ψ（a）\ | <\ | a \ | a \ | $ and $ψ$是$ ϕ $。本文的目的是将此结果扩展到更大类别的Banach空间，包括$ \ ell_p $和$ l_p $ spaces（$ 1 <p <+\ \ infty $）。在通往证明的途中，我们证明，对于上述班级中的任何Banach Space $ x $，所有忠实，Unital，可分开，反身表示$ \ Mathcal b（x）$保留等级的一台操作员实际上是同构的。
A remarkable result of Molnár [Proc. Amer. Math. Soc., 126 (1998), 853-861] states that automorphisms of the algebra of operators acting on a separable Hilbert space is stable under "small" perturbations. More precisely, if $ϕ,ψ$ are endomorphisms of $\mathcal{B}(\mathcal{H})$ such that $\|ϕ(A)-ψ(A)\|<\|A\|$ and $ψ$ is surjective then so is $ϕ$. The aim of this paper is to extend this result to a larger class of Banach spaces including $\ell_p$ and $L_p$ spaces ($1<p<+\infty$). En route to the proof we show that for any Banach space $X$ from the above class all faithful, unital, separable, reflexive representations of $\mathcal B (X)$ which preserve rank one operators are in fact isomorphisms.
