Mar 27, 2025 · I'm studying the spectral theory of unbounded operators and am trying to understand the relationship between an operator's behavior on its core and its spectrum.

A graph $X$ is a core if every homomorphism $f$ from $X$ to itself is a bijection. A subgraph $Y$ is a core of $X$ if $Y$ is a core and there exists a homomorphism from $X$ to $Y$.

May 16, 2018 · I first saw a reference to the core of an unbounded linear operator in the context of Hilbert space and subsequently in the more general context of Banach space.

Mar 9, 2021 · Given $G$ a group and $H$ a subgroup of $G$, how can I prove that $ {\rm Core}_H G:=\bigcap_ {g\in G} gHg^ {-1}$ is a normal subgroup of $G$? I've proved that is a subgroup, but …

Nov 6, 2020 · Maybe part of the difficulty is that you are using an equivalent but more inconvenient definition of $core (A)$. Let me use the following definition: $a\in core (A)$ if and only if for all $d\in …

Jun 23, 2014 · Thanks for answer! I dont understand why the kernel of the provided map: G $\rightarrow S_ {index [G:U]}$ is $core_G (U)$. Could u explain that for me? And how u get the last thing?

Feb 22, 2018 · I'm reading "A short course on Operator Semigroups" by Engel and Nagel. I came across a result about core of an operator and there is a part in which I'm stuck. On page 41, when Hahn …