| Publication type: |
 |
Preprint, Working Paper, ... |
|
| Subject: |
|
Mathematics/Functional Analysis
|
|
| Title: |
|
Numerical radius and distance from unitary operators |
|
| Author(s): |
|
Catalin Badea 1, Michel Crouzeix 2 |
|
| Laboratory: |
|
|
|
| Research team: |
|
Analyse numérique |
| Abstract: |
|
Denote by $w(A)$ the numerical radius of a bounded linear operator $A$ acting on Hilbert space. Suppose that $A$ is invertible and that $w(A)\leq 1{+}\varepsilon$ and $w(A^{-1})\leq 1{+}\varepsilon$ for some $\varepsilon\geq0$. It is shown that $\inf\{\|A{-}U\|\,: U$ unitary$\}\leq c\varepsilon^{1/4}$ for some constant $c>0$. This generalizes a result due to J.G.~Stampfli, which is obtained for $\varepsilon = 0$. An example is given showing that the exponent $1/4$ is optimal. The more general case of the operator $\rho$-radius $w_{\rho}(\cdot)$ is discussed for $1\le \rho \le 2$. |
|
| Fulltext language: |
|
English |
|
| Production date: |
|
2012-01-24 |
|
|
| ANR Project: |
|
|
|
|
Export this paper
