Brown measure and iterates of the Aluthge transform for some operators arising from measurable actions
نویسندگان
چکیده
منابع مشابه
Brown Measure and Iterates of the Aluthge Transform for Some Operators Arising from Measurable Actions∗
We consider the Aluthge transform T̃ = |T |1/2U |T |1/2 of a Hilbert space operator T , where T = U |T | is the polar decomposition of T . We prove that the map T 7→ T̃ is continuous with respect to the norm topology and with respect to the ∗–SOT topology on bounded sets. We consider the special case in a tracial von Neumann algebra when U implements an automorphism of the von Neumann algebra gen...
متن کاملOn the Aluthge Transform: Continuity Properties and Brown Measure
We consider the Alugthe transform T̃ = |T |1/2U |T |1/2 of a Hilbert space operator T , where T = U |T | is the polar decomposition of T . We prove that the map T 7→ T̃ is continuous with respect to the norm topology and with respect to the ∗–SOT topology. For T in a tracial von Neumann algebra, we show that the Brown measure is unchanged by the Aluthge transform. We consider the special case whe...
متن کاملsome properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولConvergence 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...
متن کاملSome Connections between an Operator and Its Aluthge Transform
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2009
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-09-04762-x