Correction to: Regularity properties of some perturbations of non-densely defined operators with applications

1 Correction to: J. Evol. Equ. https://doi.org/10.1007/s00028-019-00510-y

The original publication of the article contains errors which need to be amended as mentioned below:

In Sect. 6.2. “Standard assumptions and main results”, line 9, the definition of ${\mathcal {A}}$ is obviously wrong (since for $\varphi \in D({\mathcal {B}}_0)$ one must have $\varphi (0) = 0$ which makes ${\mathcal {A}}$ useless). Hence, the following lines 8–11:

should be replaced with:

Now, ${\mathcal {A}}_{X_0} = 0 \times {\mathcal {B}}_0$ (as $R(\lambda , {\mathcal {A}}_{X_0}) = R(\lambda , {\mathcal {A}})|_{X_0} = R(\lambda , {\mathcal {B}}_0)$) and Eq. (6.4) are true, and so all the following results and proofs remain unchanged.

In Lemma 2.4, last line: “Others follow from (b) and Definition 2.3” should be “Others follow from (b) and Lemma 2.3”.

In Definition 6.3, line 2: “${\mathcal {B}}_0$ is an invertible closure of” should be “${\mathcal {B}}_0$ is a closure of”.

In Example 6.13, line 5: “with $\sup _{0<a<c}\{|A(a)|,|C(a)|\} < \infty$” should be “with $\sup _{0<a<c}\{|A(a)|\} < \infty$ and $|C(\cdot )| \in L^{p'}(0, c)$ ($1/{p'} + 1/p = 1$)”.