English

Separate continuity of the Lempert function of the spectral ball

Complex Variables 2011-11-17 v2
Authors: Nikolai Nikolov , Pascal J. Thomas
View on arXiv ↗ PDF ↗

Abstract

We find all matrices AA from the spectral unit ball Ωn\Omega_n such that the Lempert function lΩn(A,⋅)l_{\Omega_n}(A,\cdot) is continuous.

Keywords

Lempert function spectral unit ball separate continuity matrix

Cite

@article{arxiv.0910.4299,
  title  = {Separate continuity of the Lempert function of the spectral ball},
  author = {Nikolai Nikolov and Pascal J. Thomas},
  journal= {arXiv preprint arXiv:0910.4299},
  year   = {2011}
}

Comments

small corrections; one reference is added

Related papers

View all related →
Complex Variables · Mathematics
Discontinuity of the Lempert function of the spectral ball
Pascal J. Thomas, Nguyen Van Trao
2009-09-07
Complex Variables · Mathematics
Discontinuity of the Lempert function and the Kobayashi--Royden metric of the spectral ball
Nikolai Nikolov, Pascal J. Thomas, Wlodzimierz Zwonek
2010-06-23
Complex Variables · Mathematics
The multipole Lempert function is monotone under inclusion of pole sets
Nikolai Nikolov, Peter Pflug
2007-05-23
Classical Analysis and ODEs · Mathematics
Discrete Uniqueness Sets for Functions with Spectral Gaps
Alexander Olevskii, Alexander Ulanovskii
2017-09-13
Complex Variables · Mathematics
Convergence and multiplicities for the Lempert function
Pascal J. Thomas, Nguyen Van Trao
2008-03-25
Functional Analysis · Mathematics
Functional continuity of unital $B_{0}$-algebras with orthogonal bases
M. El Azhari
2019-11-19
Spectral Theory · Mathematics
$\mathbf {SL_2(\bbR)}$, Exponential Herglotz Representations, and Spectral Averaging
Fritz Gesztesy, Konstantin A. Makarov
2007-05-23
Mathematical Physics · Physics
Continuity of spectral averaging
C. A. Marx
2010-09-21
Functional Analysis · Mathematics
Automatic continuity for the unitary group
Todor Tsankov
2011-09-07
General Topology · Mathematics
Separately continuous functions of many variables on product of spaces which are products of metrizable multipliers
V. K. Maslyuchenko, V. V. Mykhaylyuk
2015-12-31
Analysis of PDEs · Mathematics
The unique continuation property of sublinear equations
Nicola Soave, Tobias Weth
2017-07-25
General Mathematics · Mathematics
Delta-epsilon functions and uniform continuity on metric spaces
César Adolfo Hernández Melo
2017-10-12
Functional Analysis · Mathematics
Spectral pairs in Cartesian coordinates
Palle E. T. Jorgensen, Steen Pedersen
2007-05-23
Classical Analysis and ODEs · Mathematics
Absolute continuity of Bernoulli convolutions for algebraic parameters
Péter P. Varjú
2019-04-02
Complex Variables · Mathematics
Separate holomorphic extension along lines and holomorphic extension from the sphere to the ball
L. Baracco
2011-01-04
Complex Variables · Mathematics
Upper bound for the Lempert function of smooth domains
Nikolai Nikolov, Peter Pflug, Pascal J. Thomas
2012-09-03
Mathematical Physics · Physics
On absolute continuity of spectra of periodic elliptic operators
Peter Kuchment, Sergei Levendorski
2007-05-23
Classical Analysis and ODEs · Mathematics
Periodicity of the spectrum of a finite union of intervals
Mihail N. Kolountzakis
2011-03-01
Dynamical Systems · Mathematics
Absolute continuity of self-similar measures on the plane
Boris Solomyak, Adam Śpiewak
2023-08-31
Complex Variables · Mathematics
Green vs. Lempert functions: a minimal example
Pascal J. Thomas
2012-09-06
Functional Analysis · Mathematics
Continuity of the $L_{p}$ Balls and an Application to Input-Output System Described by the Urysohn Type Integral Operator
Anar Huseyin, Nesir Huseyin, Khalik G. Guseinov
2021-12-28
Differential Geometry · Mathematics
Regularity of the level set flow
Tobias Holck Colding, William P. Minicozzi
2016-06-17
Mathematical Physics · Physics
Schr\"{o}dinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum
Stanislav A. Molchanov, Boris R. Vainberg
2016-04-04
Rings and Algebras · Mathematics
An explicit Lipschitz constant for the joint spectral radius
Victor Kozyakin
2010-04-20
Analysis of PDEs · Mathematics
Lipschitz continuity of the eigenfunctions on optimal sets for functionals with variable coefficients
Baptiste Trey
2020-04-01