Simultaneous semi-eigenvectors for matrices over an extremal algebra

1996 ◽  
Vol 43 (1) ◽  
pp. 107-119
Author(s):  
Karl Nachtigall
Keyword(s):  
Extremal Algebra

scholarly journals Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra

1993 ◽  
Vol 35 (3) ◽  
pp. 325-326
Author(s):  
M. J. Crabb ◽  
C. M. McGregor
Keyword(s):  
Exponential Type ◽  
Line Segment ◽  
Convex Set ◽  
Numerical Range ◽  
Compact Convex ◽  
Banach Algebras ◽  
Functions Of Exponential Type ◽  
Compact Convex Set ◽  
Unital Banach Algebra ◽  
Extremal Algebra

For any compact convex set K ⊂ ℂ there is a unital Banach algebra Ea(K) generated by an element h in which every polynomial in h attains its maximum norm over all Banach algebras subject to the numerical range V(h) being contained in K, [1]. In the case of K a line segment in ℝ, we show here that Ea(K) does not have Arens regular multiplication. We also show that ideas about Ea(K) give simple proofs of, and extend, two inequalities of C. Frappier [4].

scholarly journals Endomorphisms of an extremal algebra

1988 ◽  
Vol 104 (3) ◽  
pp. 852-852 ◽  
Author(s):  
Herbert Kamowitz ◽  
Dennis Wortman
Keyword(s):  
Extremal Algebra

scholarly journals The Extremal Algebra on Two Hermitians With Square 1

2002 ◽  
Vol 44 (02) ◽  
Author(s):  
M. J. Crabb ◽  
J. Duncan ◽  
C. M. McGregor
Keyword(s):  
Extremal Algebra

scholarly journals The Arens irregularity of an extremal algebra

1994 ◽  
Vol 37 (1) ◽  
pp. 139-141
Author(s):  
M. J. Crabb ◽  
C. M. McGregor
Keyword(s):  
Banach Algebras ◽  
Extremal Algebra

A class of extremal Banach algebras has Arens irregular multiplication.

scholarly journals Robustness of Interval Monge Matrices in Fuzzy Algebra

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 652
Author(s):  
Máté Hireš ◽  
Monika Molnárová ◽  
Peter Drotár
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Interval Matrix ◽  
Monge Matrix ◽  
Fuzzy Algebra ◽  
Inexact Data ◽  
Necessary And Sufficient ◽  
Equivalent Conditions ◽  
Extremal Algebra

Max–min algebra (called also fuzzy algebra) is an extremal algebra with operations maximum and minimum. In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra. A matrix with inexact data (also called interval matrix) is a set of matrices given by a lower bound matrix and an upper bound matrix. An interval Monge matrix is the set of all Monge matrices from an interval matrix with Monge lower and upper bound matrices. There are two possibilities to define the robustness of an interval matrix. First, the possible robustness, if there is at least one robust matrix. Second, universal robustness, if all matrices are robust in the considered set of matrices. We found necessary and sufficient conditions for universal robustness in cases when the lower bound matrix is trivial. Moreover, we proved necessary conditions for possible robustness and equivalent conditions for universal robustness in cases where the lower bound matrix is non-trivial.

Sign in / Sign up

Export Citation Format

Share Document