Spherical Aluthge transform, spherical p and log-hyponormality of commuting pairs of operators

2020 ◽  
pp. 1-18
Author(s):  
Hyung Won Kim ◽  
Jaewoong Kim ◽  
Jasang Yoon
Keyword(s):  
Aluthge Transform ◽  
Commuting Pairs

scholarly journals COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET

1996 ◽  
Vol 06 (12a) ◽  
pp. 2427-2432 ◽  
Author(s):  
PAU ATELA ◽  
JUN HU
Keyword(s):  
Julia Set ◽  
Exact Relation ◽  
Complete Answer ◽  
Commuting Pairs

It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Julia set and commuting pairs.

Commuting pairs of self-adjoint elements in C *-algebras

2017 ◽  
Vol 67 (1) ◽  
pp. 209-212
Author(s):  
Osamu Hatori
Keyword(s):  
Continuous Function ◽  
Functional Calculus ◽  
Continuous Functional ◽  
C Algebras ◽  
Commuting Pairs ◽  
The Given

Abstract We give a condition on commutativity of a pair of self-adjoint elements in a C *-algebra with respect to the continuous functional calculus. We also give an answer to the question raised by Jeang and Ko that if a non-constant continuous function totally spans the given C *-algebra.

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 Quasinormality of powers of commuting pairs of bounded operators

2020 ◽  
Vol 278 (3) ◽  
pp. 108342 ◽  
Author(s):  
Raúl E. Curto ◽  
Sang Hoon Lee ◽  
Jasang Yoon
Keyword(s):  
Bounded Operators ◽  
Commuting Pairs

scholarly journals A construction of a large family of commuting pairs of integrable symplectic birational four-dimensional maps

2017 ◽  
Vol 473 (2198) ◽  
pp. 20160535 ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris
Keyword(s):  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Vector Fields ◽  
Large Family ◽  
Hamiltonian Vector ◽  
Discretization Scheme ◽  
Integrals Of Motion ◽  
Completely Integrable ◽  
Hamiltonian Vector Fields ◽  
Commuting Pairs

We give a construction of completely integrable four-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan–Hirota–Kimura discretization scheme, we arrive at pairs of birational four-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on R 4 , and possess two independent integrals of motion, which are perturbations of the original Hamilton functions and which are in involution with respect to the perturbed symplectic structure. Thus, these maps are completely integrable in the Liouville–Arnold sense. Moreover, under a suitable normalization of the original pairs of vector fields, the pairs of maps commute and share the invariant symplectic structure and the two integrals of motion.

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
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