Numerical range of Aluthge transform of operator
نویسندگان
چکیده
منابع مشابه
Some 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 کاملConvergence 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 کاملConvergence of iterated Aluthge transform sequence for diagonalizable matrices
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∞...
متن کاملOn the Closure of the Numerical Range of an Operator
If T is a bounded linear mapping (briefly, operator) in a Hilbert space 3C, the numerical range of T is the set WiT) = {(Tx, x): |[x|| = l}; thus WiT) is convex [8, p. 131], and its closure clfW^r)] is compact and convex. Roughly speaking, in this note we observe that cl[TF(T)] can be uniquely defined for an element T of an abstract C*-algebra, while WiT) cannot. The C*-algebra setting yields a...
متن کاملNumerical Range of the Derivation of an Induced Operator
Let V be an n-dimensional inner product space over C, let H be a subgroup of the symmetric group on {1, . . . , m}, and let χ : H → C be an irreducible character. Denote by V m χ (H) the symmetry class of tensors over V associated with H and χ. Let K(T ) ∈ End (V m χ (H)) be the operator induced by T ∈ End (V ), and let DK(T ) be the derivation operator of T . The decomposable numerical range W...
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: Linear Algebra and its Applications
سال: 2002
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00361-0