Maps preserving the nilpotency of products of operators
نویسندگان
چکیده
منابع مشابه
Maps preserving the nilpotency of products of operators
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N (X) be the set of nilpotent operators in B(X). Suppose φ : B(X)→ B(X) is a surjective map such that A,B ∈ B(X) satisfy AB ∈ N (X) if and only if φ(A)φ(B) ∈ N (X). If X is infinite dimensional, then there exists a map f : B(X)→ C \ {0} such that one of the following holds: (a) There is a bijective bounded li...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.11.013