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

The Original Article was published on 29 April 2019

## 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 $$|C(\cdot )| \in L^{p'}(0, c)$$ ($$1/{p'} + 1/p = 1$$)”.

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Correspondence to Deliang Chen.

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