On the Range of the Aluthge Transform |
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Authors: | Guoxing Ji Yongfeng Pang Ze Li |
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Affiliation: | (1) College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710062, People’s Republic of China |
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Abstract: | Let be the algebra of all bounded linear operators on a complex separable Hilbert space For an operator let be the Aluthge transform of T and we define for all where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range of Δ. We prove that R(Δ) is neither closed nor dense in However R(Δ) is strongly dense if is infinite dimensional. An erratum to this article is available at . |
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Keywords: | Primary 47A15 Secondary 47B20 |
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