Let B（X） be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n 〉 1, we show that an additive surjective map Ф on B（X） preserves Drazin inver...Let B（X） be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n 〉 1, we show that an additive surjective map Ф on B（X） preserves Drazin invertible operators of index non-greater than n in both directions if and only if Ф is either of the form Ф（T） = aATA-1 or of the form Ф（T） = aBT＊B-1 where a is a non-zero scalar, A ： X → X and B ： X＊ → X are two bounded invertible linear or conjugate linear operators.展开更多
文摘Let B（X） be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. Given an integer n 〉 1, we show that an additive surjective map Ф on B（X） preserves Drazin invertible operators of index non-greater than n in both directions if and only if Ф is either of the form Ф（T） = aATA-1 or of the form Ф（T） = aBT＊B-1 where a is a non-zero scalar, A ： X → X and B ： X＊ → X are two bounded invertible linear or conjugate linear operators.
