Equations arising from Jordan *-derivation pairs |
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Authors: | Email author" target="_blank">Dijana?Ili?evi?Email author |
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Institution: | (1) Department of Mathematics, University of Zagreb, Bijenika 30, P.O. Box 335, 10002 Zagreb, Croatia |
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Abstract: | Summary.
We study certain functional equations derived from the
definition of a Jordan *-derivation pair.
More precisely, if A is a complex
*-algebra and M is a
bimodule over A, having the structure of a complex vector space
compatible with the structure of A,
such that
implies
m = 0 and
implies m
= 0 and
if
are unknown additive mappings satisfying
then E and
F can be represented by double centralizers. The
obtained result implies that one of the equations in the
definition of a Jordan *-derivation pair is redundant.
Furthermore, a remark on the extension of this result to unknown
additive mappings
such that
is given in a special case. |
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Keywords: | Primary 46K 39B52 Secondary 16W25 47B47 |
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