Abstract
Associated with every operator T on Hilbert space is its Aluthge transform T̃ (defined below). In this note we study various connections between T and T̃, including relations between various spectra, numerical ranges, and lattices of invariant subspaces. In particular, we show that if T̃ has a nontrivial invariant subspace, then so does T, and we give various applications of our results.
| Original language | English |
|---|---|
| Pages (from-to) | 437-448 |
| Number of pages | 12 |
| Journal | Integral Equations and Operator Theory |
| Volume | 37 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2000 |
Bibliographical note
Funding Information:Acknowledgement. This paper was written while the second and the third authors were visiting Kyungpook National University in Taegu, Korea in 1998, and these authors wish to express their thanks to that university for its warm hospitality during their visit. The first author was supported by TGRC-KOSEF and KOSEF grant 94-0701-02-01-3. The second author was supported by the MOST through National R&D program (97-N6-01-01-A-5) for Women's Universities. The third author acknowledges support from the National Science Foundation.