Let X be a complex Banach space. If 8: B(X) Γ B(X) is a surjective linear map such that A and 8(A) have the same spectral radius for every A # B(X), then 8=c3 where 3 is either an algebra-automorphism or an antiautomorphism of B(X) and c is a complex constant such that |c|=1.
Linear maps preserving the essential spectral radius
β Scribed by M. Bendaoud; A. Bourhim; M. Sarih
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 92 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
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β¦ Synopsis
Let L(H) be the algebra of all bounded linear operators on an infinite dimensional complex Hilbert H. We characterize linear maps from L(H) onto itself that preserve the essential spectral radius.
π SIMILAR VOLUMES
Define the sign-real spectral radius of a real n Γ n matrix A as Ο s 0 (A) = max SβS Ο 0 (SA), where Ο 0 (A) = max{|Ξ»|; Ξ» a real eigenvalue of A} is the real spectral radius of A and S denotes the set of signature matrices, i.e. S = {S; |S| = I}, the absolute value of matrices being meant entrywise.
Let M + n be the set of entrywise nonnegative n Γ n matrices. Denote by r(A) the spectral radius (Perron root) of A β M + n . Characterization is obtained for maps f : In particular, it is shown that such a map has the form for some S β M + n with exactly one positive entry in each row and each co
Let M n (F) be the space of all n Γ n matrices over a field F of characteristic not 2, and let P n (F) be the subset of M n (F) consisting of all n Γ n idempotent matrices. We denote by n (F) the set of all maps from M n (F) to itself satisfying A -Ξ»B β P n (F) if and only if Ο(A)Ξ»Ο(B) β P n (F) for