Remarks on Essential Maximal Numerical Range of 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...
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 کاملOn the decomposable numerical range of operators
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi :Hrightarrow mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{chi}(H)$ the symmetry class of tensors associated with $H$ and $chi$. Let $K(T)in (V_{chi}(H))$ be the operator induced by $Tin text{End}(V)$. Th...
متن کاملRemarks on Numerical Semigroups
We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights stated in [To]. 0. Introduction Let H be a numerical semigroup, that is, a subsemigroup of (N,+) whose complement is finite. Examples of such semigroups are the Weierstras...
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 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: International Journal of Pure Mathematical Sciences
سال: 2019
ISSN: 2297-6205
DOI: 10.18052/www.scipress.com/ijpms.20.1