On centralizers of standard operator algebras with involution
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Maja Fosner
maja.fosner@fl.uni-mb.si
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Benjamin Marcen
benjamin.marcen@fl.uni-mb.si
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Nejc Sirovnik
nejc.sirovnik@uni-mb.si
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DOI:
https://doi.org/10.4067/S0719-06462013000300005Abstract
The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Let T : A(X) → L(X) be a linear mapping satisfying the relation 2T(AA∗A) = T(A)A∗A + AA∗T(A) for all A ∈ A(X). In this case T is of the form T(A) = λA for all A ∈ A(X), where λ is some fixed complex number.
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Published
2013-10-01
How to Cite
[1]
M. Fosner, B. Marcen, and N. Sirovnik, “On centralizers of standard operator algebras with involution”, CUBO, vol. 15, no. 3, pp. 45–50, Oct. 2013.
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