Fuglede–Putnam type theorems via the Aluthge transform
نویسندگان
چکیده
منابع مشابه
Convergence of iterated Aluthge transform sequence for diagonalizable matrices II: λ-Aluthge transform
Let λ ∈ (0, 1) and let T be a r × r complex matrix with polar decomposition T = U |T |. Then, the λAluthge transform is defined by ∆λ (T ) = |T | U |T |. Let ∆nλ(T ) denote the n-times iterated Aluthge transform of T , n ∈ N. We prove that the sequence {∆nλ(T )}n∈N converges for every r × r diagonalizable matrix T . We show regularity results for the two parameter map (λ, T ) 7→ ∆∞λ (T ), and w...
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Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then, the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. We prove that the sequence {∆n(T )}n∈N converges for every r× r diagonalizable matrix T . We show that the limit ∆∞(·) is a map of class C∞...
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Associated with T = U|T | (polar decomposition) in L(H) is a related operator T̃ = |T | 1 2U|T | 1 2 , called the Aluthge transform of T . In this paper we study some connections betweenT and T̃ , including the following relations; the single valued extension property, an analogue of the single valued extension property onWm(D,H), Dunford’s property (C) and the property (β). 2000 Mathematics Subj...
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ژورنال
عنوان ژورنال: Positivity
سال: 2012
ISSN: 1385-1292,1572-9281
DOI: 10.1007/s11117-011-0154-4