On centralizers of standard operator algebras with involution

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DOI:

https://doi.org/10.4067/S0719-06462013000300005

Abstract

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.

Keywords

ring , ring with involution , prime ring , semiprime ring , Banach space , Hilbert space , standard operator algebra , H∗-algebra , left (right) centralizer , two-sided centralizer
  • Maja Fosner Faculty of Logistics, University of Maribor, Mariborska cesta 7 3000 Celje Slovenia.
  • Benjamin Marcen Faculty of Logistics, University of Maribor, Mariborska cesta 7 3000 Celje Slovenia.
  • Nejc Sirovnik Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska cesta 160 2000 Maribor Slovenia.
  • Pages: 45-50
  • Date Published: 2013-10-01
  • Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

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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.

Issue

Vol. 15 No. 3 (2013): CUBO, A Mathematical Journal

Section

Articles