Spectra of the spherical Aluthge transform, the linear pencil, and a commuting pair of operators

2020 ◽  
pp. 1-18
Author(s):  
Slaviša V. Djordjević ◽  
Jaewoong Kim ◽  
Jasang Yoon
Keyword(s):  
Aluthge Transform ◽  
Linear Pencil

A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves

2016 ◽  
Vol 68 (1) ◽  
pp. 67-87
Author(s):  
Hirotaka Ishida
Keyword(s):  
Lower Bound ◽  
General Type ◽  
Hyperelliptic Curves ◽  
Surfaces Of General Type ◽  
Linear Pencil ◽  
Surface Of General Type

AbstractLet S be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration whose slope is less than or equal to four, we give a lower bound on the Euler–Poincaré characteristic of S. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.

scholarly journals The Aluthge transform of unilateral weighted shifts and the Square Root Problem for finitely atomic measures

2019 ◽  
Vol 292 (11) ◽  
pp. 2352-2368 ◽  
Author(s):  
Raúl E. Curto ◽  
Jaewoong Kim ◽  
Jasang Yoon
Keyword(s):  
Square Root ◽  
Weighted Shifts ◽  
Aluthge Transform

scholarly journals Convergence of the Iterated Aluthge Transform Sequence for Diagonalizable Matrices II: λ-Aluthge Transform

2008 ◽  
Vol 62 (4) ◽  
pp. 465-488 ◽  
Author(s):  
Jorge Antezana ◽  
Enrique Pujals ◽  
Demetrio Stojanoff
Keyword(s):  
Aluthge Transform

On the numerical range behavior under the generalized Aluthge transform

2008 ◽  
Vol 56 (1-2) ◽  
pp. 163-177
Author(s):  
David E. V. Rose ◽  
Ilya M. Spitkovsky
Keyword(s):  
Numerical Range ◽  
Aluthge Transform

scholarly journals Parallelism between Moore-Penrose inverse and Aluthge transformation of operators

2018 ◽  
Vol 12 (2) ◽  
pp. 318-335 ◽  
Author(s):  
M.R. Jabbarzadeh ◽  
H. Emamalipour ◽  
Sohrabi Chegeni
Keyword(s):  
Hilbert Space ◽  
Multiplication Operators ◽  
Aluthge Transform ◽  
Aluthge Transformation

In this paper we study some parallelisms between ?-Aluthge transform and binormal operators on a Hilbert space via the Moore-Penrose inverse. Moreover, we give some applications of these results on the Lambert multiplication operators acting on L2(?).

scholarly journals Generalizations of the Aluthge transform of operators

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6465-6474 ◽  
Author(s):  
Khalid Shebrawi ◽  
Mojtaba Bakherad
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Convex Function ◽  
Polar Decomposition ◽  
Continuous Functions ◽  
Complex Hilbert Space ◽  
Numerical Radius ◽  
Aluthge Transform ◽  
Bounded Linear ◽  
Definition Of

Let A be an operator with the polar decomposition A = U|A|. The Aluthge transform of the operator A, denoted by ?, is defined as ? = |A|1/2U |A|1/2. In this paper, first we generalize the definition of Aluthge transformfor non-negative continuous functions f,g such that f(x)g(x) = x (x ? 0). Then, by using this definition, we get some numerical radius inequalities. Among other inequalities, it is shown that if A is bounded linear operator on a complex Hilbert space H, then h (w(A)) ? 1/4||h(g2 (|A|)) + h(f2(|A|)|| + 1/2h (w(? f,g)), where f,g are non-negative continuous functions such that f(x)g(x) = x (x ? 0), h is a non-negative and non-decreasing convex function on [0,?) and ? f,g = f (|A|)Ug(|A|).

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