For an odd prime number p, and positive integers k and , we denote , a digraph for which is the set of vertices and there is a directed edge from u to v if , where . In this work, we study isolated and non...For an odd prime number p, and positive integers k and , we denote , a digraph for which is the set of vertices and there is a directed edge from u to v if , where . In this work, we study isolated and non-isolated fixed points (or loops) in digraphs arising from Discrete Lambert Mapping. It is shown that if , then all fixed points in are isolated. It is proved that the digraph has isolated fixed points only if . It has been characterized that has no cycles except fixed points if and only if either g is of order 2 or g is divisible by p. As an application of these loops, the solvability of the exponential congruence has been discussed.展开更多
In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach ...In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.展开更多
A structural feature of multiplicative maps on B( X ) which sends some rank 1 operator to an operator of rank not greater than 1 is given, and based on it, some characterizations of automorphism of B( X ) are obtained...A structural feature of multiplicative maps on B( X ) which sends some rank 1 operator to an operator of rank not greater than 1 is given, and based on it, some characterizations of automorphism of B( X ) are obtained and some multiplicative preserver problems are answered.展开更多
Let X be a compact metric space and let Lip（X） be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip（X）, σπ（f） denotes the peripheral spectrum of ...Let X be a compact metric space and let Lip（X） be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip（X）, σπ（f） denotes the peripheral spectrum of f. We state that any map Φ from Lip（X） onto Lip（Y） which preserves multiplicatively the peripheral spectrum： σπ（Φ（f）Φ（g）） = σπ（fg）, A↓f, g ∈ Lip（X） is a weighted composition operator of the form Φ（f） = τ· （f °φ） for all f ∈ Lip（X）, where τ ： Y → {-1, 1} is a Lipschitz function and φ ： Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip（X）-algebras is of the form above.展开更多
In this paper,we show that every injective Jordan semi-triple multiplicative map on the Hermitian matrices must be surjective,and hence is a Jordan ring isomorphism.
文摘For an odd prime number p, and positive integers k and , we denote , a digraph for which is the set of vertices and there is a directed edge from u to v if , where . In this work, we study isolated and non-isolated fixed points (or loops) in digraphs arising from Discrete Lambert Mapping. It is shown that if , then all fixed points in are isolated. It is proved that the digraph has isolated fixed points only if . It has been characterized that has no cycles except fixed points if and only if either g is of order 2 or g is divisible by p. As an application of these loops, the solvability of the exponential congruence has been discussed.
文摘In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.
文摘A structural feature of multiplicative maps on B( X ) which sends some rank 1 operator to an operator of rank not greater than 1 is given, and based on it, some characterizations of automorphism of B( X ) are obtained and some multiplicative preserver problems are answered.
基金MEC project MTM2006-4837Junta de Andalucia projects P06-FQM-1215 and P06-FQM-1438
文摘Let X be a compact metric space and let Lip（X） be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip（X）, σπ（f） denotes the peripheral spectrum of f. We state that any map Φ from Lip（X） onto Lip（Y） which preserves multiplicatively the peripheral spectrum： σπ（Φ（f）Φ（g）） = σπ（fg）, A↓f, g ∈ Lip（X） is a weighted composition operator of the form Φ（f） = τ· （f °φ） for all f ∈ Lip（X）, where τ ： Y → {-1, 1} is a Lipschitz function and φ ： Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip（X）-algebras is of the form above.
基金Supported by the National Natural Science Foundation of China (Grant Nos.11001194 10771157)the Natural Science Foundation of Shanxi Province (Grant No.2009021002)
文摘In this paper,we show that every injective Jordan semi-triple multiplicative map on the Hermitian matrices must be surjective,and hence is a Jordan ring isomorphism.
