LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we de...LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we denote the F-space of all n×n matrices over R and the set of all idempotentmatrices in M<sub>n</sub>（R）, respectively. If a linear map L from M<sub>n</sub>（R） to M<sub>m</sub>（R<sub>1</sub>） satisfies L（I<sub>n</sub>（R）） I<sub>m</sub>（R<sub>1</sub>） we call L an idempotence preserver （all such maps will be denoted byL<sub>n</sub>, m（R,R<sub>1</sub>））. To determine the forms of idempotence preservers is one important展开更多
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
文摘LET R and R<sub>1</sub> be skew-fields with centres F and F<sub>1</sub>, where F F<sub>1</sub> and |F|】2. By M<sub>n</sub> （R）and I<sub>n</sub>（R） we denote the F-space of all n×n matrices over R and the set of all idempotentmatrices in M<sub>n</sub>（R）, respectively. If a linear map L from M<sub>n</sub>（R） to M<sub>m</sub>（R<sub>1</sub>） satisfies L（I<sub>n</sub>（R）） I<sub>m</sub>（R<sub>1</sub>） we call L an idempotence preserver （all such maps will be denoted byL<sub>n</sub>, m（R,R<sub>1</sub>））. To determine the forms of idempotence preservers is one important
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.
