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  • 1 University of Maribor, PEF Department of Mathematics Koroška 160 2000 Maribor Slovenia
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In this paper we 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 , and let A ( X ) ⊂ L ( X ) be a standard operator algebra. Suppose we have a linear mapping D : A ( X ) → L ( X ) satisfying the relation D ( A3 ) = D ( A ) A2 + AD ( A ) A + A2D ( A ), for all AA ( X ). In this case D is of the form D ( A ) = ABBA , for all AA ( X ) and some BL ( X ). We apply this result, which generalizes a classical result of Chernoff, to semisimple H *-algebras.

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