Denote by B(X) the Banach algebra of all bounded linear operators on a complex Banach space X. In this paper, the representation of weakly continuous linear maps on B(X) which maps rank-1 operators to operators of ran...Denote by B(X) the Banach algebra of all bounded linear operators on a complex Banach space X. In this paper, the representation of weakly continuous linear maps on B(X) which maps rank-1 operators to operators of rank at most 1 is given, and sequentially, some representation theorems for rank-preserving linear maps, spectrum-preserving linear maps and positivity-preserving linear maps on B(X) are obtained.展开更多
After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is u...After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.展开更多
Let S be a finite linear space, and let G be a group of automorphisms of S. If G is soluble and line-transitive, then for a given k but a finite number of pairs of ( S, G), S has v= pn points and G≤AΓ L(1,pn).
文摘Denote by B(X) the Banach algebra of all bounded linear operators on a complex Banach space X. In this paper, the representation of weakly continuous linear maps on B(X) which maps rank-1 operators to operators of rank at most 1 is given, and sequentially, some representation theorems for rank-preserving linear maps, spectrum-preserving linear maps and positivity-preserving linear maps on B(X) are obtained.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10471152).
文摘After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.
文摘Let S be a finite linear space, and let G be a group of automorphisms of S. If G is soluble and line-transitive, then for a given k but a finite number of pairs of ( S, G), S has v= pn points and G≤AΓ L(1,pn).
