On the Range of the Aluthge Transform |
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Authors: | Guoxing Ji Yongfeng Pang Ze Li |
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Institution: | (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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