论文标题
在表示和图形的光谱上。勘误
On spectra of representations and graphs. Erratum
论文作者
论文摘要
不幸的是，[1]定理1的主要结果证明存在缺陷。也就是说，在命题证明11中使用的引理13仅在额外的假设下是正确的，即操作员$ a $是正常的（对于$ l^2（\ Mathbb n）$中的单方面移位操作员的伴随提供了反例）。下面我们证明了引理13的版本，该版本不需要正态性假设并将其应用于命题11。我们还在这里解释了如何使用Lemma 13的新版本来纠正[2]的定理1.6的证明。
Unfortunately the proof of the main result of [1], Theorem 1, has a flaw. Namely, Lemma 13 used in the proof of Proposition 11 is correct only under an additional assumption that the operator $A$ is normal (adjoint for the one-sided shift operator in $l^2(\mathbb N)$ provides a counterexample). Below we prove a version of Lemma 13 that does not require the normality assumption and apply it to prove Proposition 11. In addition, the same version of the lemma appears in paper [2] (as Lemma 3.1) where it is used in the proof of Theorem 1.6. We also explain here how to use the new version of Lemma 13 to correct the proof of Theorem 1.6 from [2].
