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Let $E$ be a Banach lattice. Then $u \in E_+$ is said to be a quasi-interior point of $E$ is $$E_u:=\{f \in E:\exists\, c\geq 0 \text{ such that } |f| \leq cu\}$$ is dense in $E.$ Let $\Omega$ be …

I asked this question on Math SE but didn't receive any response. Let $(T_t)$ be a $C_0$-semigroup on a Banach space $X$ with generator $A.$ If $\lambda_0\in \mathbb{C}$ is such that $e^{\lambda_0 t} …

I had asked this question on MSE but did not get any response. I would like some reference to books that talk about irreducible operators on Banach lattices and its properties. A quick google searc …

Let $A:D(A)\subseteq E \to E$ be a closed operator on a complex Banach lattice $E.$ Then $A$ is said to be real if $x+iy \in D(A) \implies x,y \in D(A)$ for all $x,y \in E_{\mathbb R}$ and $A(D(A) …

I have a doubt in proof of Lemma $4.7$ of this paper. Lemma: Let $A$ be a closed operator on a complex Banach space $E$ and assume that $0$ is an eigenvalue of $A$ and a pole of the resolvent $R(\c …

I had asked this question on Mathematics Stack Exchange, $2$ days ago but it got no response so I'm asking here. If $A$ is a closed operator, then the peripheral spectrum of $A$ is defined to be al …