Aluthge transforms of operators |
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| Authors: | Il Bong Jung Eungil Ko Carl Pearcy |
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| Institution: | (1) Department of Mathematics, Kyungpook National University, 702-701 Taegu, Korea;(2) Department of Mathematics, Ewha Women's University, 120-750 Seoul, Korea;(3) Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA |
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| Abstract: | Associated with every operatorT on Hilbert space is its Aluthge transform
(defined below). In this note we study various connections betweenT and
, including relations between various spectra, numerical ranges, and lattices of invariant subspaces. In particular, we show that if
has a nontrivial invariant subspace, then so doesT, and we give various applications of our results. |
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| Keywords: | 47A15 47B20 |
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