All Questions

The Wiener Tauberian Theorem gives condition on an $f\in L^1(\mathbb{R})$ such that the "induced 1-parameter family" $\{T_b(f)\}_{b\in \mathbb{R}}$ has a dense span in $L^1(\mathbb{R})$; ...

One sided Shift Let be $M$ separable metric space. Consider $X=M^{\mathbb{N}}$ the sequence space equipped with the product metric $d(x,y)=\sum_{i=1}^\infty |x_i-y_i|/2^i$ . Define the shift map $\...

Let $T$ be a bounded linear operator on a complex Banach space $X$. I am looking for a reference for the following result: Theorem 1. Let $p \in [1,\infty]$. The following assertions are equivalent: (...

Let $E$ be a separable Banach space and let $T\in L(E,E)$. Is there a condition on $T$ ensuring that: $$ \mbox{$\{x_n\}_{n=1}^N\subseteq E$ is linearly independent} \Rightarrow \{T(x_n)\}_{n=1}^N\cup \...

It is well-known that the weighted backshift operator $B_{\lambda}:\ell^p \rightarrow \ell^p$ is hypercyclic (with $\lambda>1$); that is, there exists a dense set of sequences $X\subseteq \ell^p$ ...

I apologize if the following is trivial for experts in the field. If so, please feel free to refer me instead to any proper references. I would like to compute the spectrum of a known non-normal, ...