λ-Aluthge transforms and Schatten ideals
Let T∈L(H), and let T = U|T| = |T*|U be the polar decomposition of T. Then, for every λ ∈ [0, 1] the λ-Aluthge transform is defined by Δλ(T) = |T|λU|T| 1-λ. We show that several properties which are known for the usual Aluthge transform (i.e. the case λ = 1/2) also hold for λ-Aluthge transforms with...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2005 |
| Country: | Argentina |
| Institution: | Universidad Nacional de La Plata |
| Repository: | SEDICI (UNLP) |
| Language: | English |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/83154 |
| Online Access: | http://sedici.unlp.edu.ar/handle/10915/83154 |
| Access Level: | Open access |
| Keyword: | Matemática Aluthge transform Polar decomposition Riesz calculus Schatten norms |
| Summary: | Let T∈L(H), and let T = U|T| = |T*|U be the polar decomposition of T. Then, for every λ ∈ [0, 1] the λ-Aluthge transform is defined by Δλ(T) = |T|λU|T| 1-λ. We show that several properties which are known for the usual Aluthge transform (i.e. the case λ = 1/2) also hold for λ-Aluthge transforms with λ ∈ (0, 1). Moreover, we get several results which are new, even for the usual Aluthge transform. |
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