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:

figurea

should be replaced with:

figureb

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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Chen, D. Correction to: Regularity properties of some perturbations of non-densely defined operators with applications. J. Evol. Equ. 20, 703–704 (2020). https://doi.org/10.1007/s00028-020-00586-x

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