The functional equation of multiplicative derivation is superstable on standard operator algebras |
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Authors: | Peter ?emrl |
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Institution: | (1) Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia |
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Abstract: | LetX be a real or complex infinite dimensional Banach space andA a standard operator algebra onX. Denote byB(X) the algebra of all bounded linear operators onX. Let : + + be a function with the property lim
t![rarr](/content/k19q7172u711pp56/xxlarge8594.gif) (t)t
–1=0. Assume that a mappingD:A B(X) satisfies D(AB)–AD(B)–D(A)B < ( A B ) for all operatorsA, B D (no linearity or continuity ofD is assumed). ThenD is of the formD(A)=AT–TA for someT B(X).This work was supported by the Research Council of Slovenia |
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