# On the Modulus of C. J. Read's Operator

On the Modulus of C. J. Read's Operator Let $$T:\ell _1 \to \ell _1$$ be the quasinilpotent operator without an invariant subspace constructed by C. J. Read. We prove that the modulus of this operator has an invariant subspace (and even an eigenvector). This answers a question posed by Y. Abramovich, C. Aliprantis and O. Burkinshaw. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# On the Modulus of C. J. Read's Operator

, Volume 2 (3) – Oct 7, 2004
8 pages

Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009790722046
Publisher site
See Article on Publisher Site

### Abstract

Let $$T:\ell _1 \to \ell _1$$ be the quasinilpotent operator without an invariant subspace constructed by C. J. Read. We prove that the modulus of this operator has an invariant subspace (and even an eigenvector). This answers a question posed by Y. Abramovich, C. Aliprantis and O. Burkinshaw.

### Journal

PositivitySpringer Journals

Published: Oct 7, 2004

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