Skip to main content
MathOverflow

Return to Question

added 70 characters in body
Source Link
Luffy
Luffy
  • 1
  • 1

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empty, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there a Banach space $Y$ and an operator $S_{T} \in L(Y)$ (which is a function of $T$) with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$? and $\mbox{iso}\,\sigma(S_{T})=\emptyset.$

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empty, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there a Banach space $Y$ and an operator $S_{T} \in L(Y)$ with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$?

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empty, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there a Banach space $Y$ and an operator $S_{T} \in L(Y)$ (which is a function of $T$) with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$ and $\mbox{iso}\,\sigma(S_{T})=\emptyset.$

added 24 characters in body
Source Link
Luffy
Luffy
  • 1
  • 1

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non emptempty, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there a Banach space $Y$ and an operator $S_{T} \in L(X)$$S_{T} \in L(Y)$ with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$?

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empt, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there an operator $S_{T} \in L(X)$ with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$?

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empty, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there a Banach space $Y$ and an operator $S_{T} \in L(Y)$ with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$?

Source Link
Luffy
Luffy
  • 1
  • 1

The non empty set of accumulation points of a bounded linear operator is the spectrum of another operator

Let $X$ be an infinite dimensional Banach space, and let $T \in L(X)$ such that the set of accumulation points of $T$ is non empt, i-e $\mbox{acc}\,\sigma(T)\neq 0.$\ Is there an operator $S_{T} \in L(X)$ with $\sigma(S_{T})=\mbox{acc}\,\sigma(T)$?