Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm eleme...Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm element,the Weyl element and the Browder element.Further,for a∈A,we give the Weyl’s theorem and the Browder’s theorem for a,and characterize necessary and sufficient conditions that both a and f(a)satisfy the Weyl’s theorem or the Browder’s theorem,where f is a complex-valued function analytic on a neighborhood ofσ(a).In addition,the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.展开更多
For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all...For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.展开更多
In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. I...In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.展开更多
文摘Denote a semisimple Banach algebra with an identity e by A.This paper studies the Fredholm,Weyl and Browder spectral theories in a semisimple Banach algebra,and meanwhile considers the properties of the Fredholm element,the Weyl element and the Browder element.Further,for a∈A,we give the Weyl’s theorem and the Browder’s theorem for a,and characterize necessary and sufficient conditions that both a and f(a)satisfy the Weyl’s theorem or the Browder’s theorem,where f is a complex-valued function analytic on a neighborhood ofσ(a).In addition,the perturbations of the Weyl’s theorem and the Browder’s theorem are investigated.
文摘For any finite-dimensional complex semisimple Lie algebra, two ellipsoids (primary and secondary) are considered. The equations of these ellipsoids are Diophantine equations, and the Weyl group acts on the sets of all their Diophantine solutions. This provides two realizations (primary and secondary) of the Weyl group on the sets of Diophantine solutions of the equations of the ellipsoids. The primary realization of the Weyl group suggests an order on the Weyl group, which is stronger than the Chevalley-Bruhat ordering of the Weyl group, and which provides an algorithm for the Chevalley-Bruhat ordering. The secondary realization of the Weyl group provides an algorithm for constructing all reduced expressions for any of its elements, and thus provides another way for the Chevalley-Bruhat ordering of the Weyl group.
基金both The Research Affairs (Research Project No.850709)The Center of Excellence for Mathematics of the University of Isfahan
文摘In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.
