Dear friends, I would like to find the spectrum of the linear operator ##A\in\mathscr{L}(\ell_2,\ell_2)##, which I have verified to be compact and eigenvalueless, defined by(adsbygoogle = window.adsbygoogle || []).push({});

##A(x_1,x_2,x_3,...,x_n,...)=(0,x_1,\frac{1}{2}x_2,...,\frac{1}{n-1}x_{n-1},...)##but my book does not give examples of how to do so. Could anybody help me in finding its (continuous) spectrum, i.e. the set ##\sigma(A)=\{\lambda\in\mathbb{C}\quad|\quad\nexists B\in\mathscr{L}(\ell_2,\ell_2):B=(A-\lambda I)^{-1}\}##?

##\infty## thanks!

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spectrum of ##(x_1,x_2,x_3, )\mapsto(0,x_1,2^{-1}x_2, )##

Loading...

Similar Threads - Spectrum mapsto 1}x_2 | Date |
---|---|

I [0,1) --> S^1 and [0,1] -->S^1 | Sep 18, 2017 |

A Convolution operator spectrum | Sep 15, 2017 |

I Simplicial complex geometric realization 1-manifold | Aug 26, 2017 |

Spectrum of a linear operator on a Banach space | May 6, 2013 |

Wide frequency spectrum problem | Mar 18, 2013 |

**Physics Forums - The Fusion of Science and Community**