Original scientific paper

https://doi.org/10.3336/gm.44.2.11

On some functional equations on standard operator algebras

Irena Kosi-Ulbl ; Faculty of Mechanical Engineering, University of Maribor, Smetanova ul. 17, Maribor, Slovenia
Joso Vukman ; Department of Mathematics and Computer Science, FNM, University of Maribor, Koroska 160, Maribor, Slovenia

Abstract

The main purpose of this paper is to prove the following result. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators on X, let A(X) L(X) be a standard operator algebra, and let T : A(X) → L(X) be an additive mapping satisfying the relation T(A2n+1) = ∑i=12n+1 (-1)i+1 Ai-1 T(A) A2n+1-i, for all A A(X) and some fixed integer n ≥ 1. In this case T\ is of the form T(A) = AB + BA, for all A A(X) and some fixed B L(X). In particular, T is continuous.

Keywords

Prime ring; semiprime ring; Banach space; standard operator algebra

Hrčak ID:

44055

URI

https://hrcak.srce.hr/44055

Publication date:

9.12.2009.

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