Inverse numerical range and Abel-Jacobi map of Hermitian determinantal representation

2021 ◽  
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato
Keyword(s):  
Numerical Range ◽  
Determinantal Representation

Inverse numerical range and determinantal representation

2018 ◽  
Vol 558 ◽  
pp. 79-100 ◽  
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato ◽  
Lina Yeh
Keyword(s):  
Numerical Range ◽  
Determinantal Representation

scholarly journals Inverse Numerical Range and Determinantal Quartic Curves

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2119
Author(s):  
Mao-Ting Chien ◽  
Hiroshi Nakazato
Keyword(s):  
Elliptic Curve ◽  
Vector Function ◽  
Numerical Range ◽  
Symmetric Matrix ◽  
Group Structure ◽  
Theta Functions ◽  
Matrix Pencil ◽  
Determinantal Representation ◽  
Ternary Form ◽  
Quartic Curves

A hyperbolic ternary form, according to the Helton–Vinnikov theorem, admits a determinantal representation of a linear symmetric matrix pencil. A kernel vector function of the linear symmetric matrix pencil is a solution to the inverse numerical range problem of a matrix. We show that the kernel vector function associated to an irreducible hyperbolic elliptic curve is related to the elliptic group structure of the theta functions used in the Helton–Vinnikov theorem.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

a-Numerical range on $$C^*$$-algebras

Positivity ◽  
2021 ◽  
Author(s):  
Abdellatif Bourhim ◽  
Mohamed Mabrouk
Keyword(s):  
Numerical Range ◽  
C Algebras

On the maximal numerical range of the bimultiplication M2,A,B

2021 ◽  
pp. 1-8
Author(s):  
Abderrahim Baghdad ◽  
Chraibi Kaadoud Mohamed
Keyword(s):  
Numerical Range

scholarly journals $L$-ideals and numerical range preservation

1977 ◽  
Vol 21 (2) ◽  
pp. 365-373 ◽  
Author(s):  
C. K. Chui ◽  
P. W. Smith ◽  
R. R. Smith ◽  
J. D. Ward
Keyword(s):  
Numerical Range
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