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Maps preserving the nilpotency of products of operators

✍ Scribed by Chi-Kwong Li; Peter Šemrl; Nung-Sing Sze


Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
205 KB
Volume
424
Category
Article
ISSN
0024-3795

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Let B(X) be the algebra of bounded operators on a complex infinite dimensional Banach space X, and F (X) be the subalgebra of all finite rank operators in B(X). A characterization of additive mappings on F (X) which preserve rank one nilpotent operators in both directions is given. As applications o

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Let H be a complex Hilbert space of dimension greater than 2 and J ∈ B(H) be an invertible self-adjoint operator. Denote by A † = J -1 A \* J the indefinite conjugate of A ∈ B(H) with respect to J and denote by w(A) the numerical radius of A. Let W and V be subsets of B(H) which contain all rank one