×

zbMATH — the first resource for mathematics

Lie \(\ast\)-homomorphisms between Lie \(C^*\)-algebras and Lie \(\ast\)-derivations on Lie \(C^*\)-algebras. (English) Zbl 1051.46052
Summary: We prove the generalized Hyers-Ulam-Rassias stability of Lie \(\ast\)-homomorphisms in Lie \(C^*\)-algebras, and of Lie \(\ast\)-derivations on Lie \(C^*\)-algebras.

MSC:
46L70 Nonassociative selfadjoint operator algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Găvruta, P., A generalization of the hyers – ulam – rassias stability of approximately additive mappings, J. math. anal. appl., 184, 431-436, (1994) · Zbl 0818.46043
[2] Jun, K.; Lee, Y., A generalization of the hyers – ulam – rassias stability of Jensen’s equation, J. math. anal. appl., 238, 305-315, (1999) · Zbl 0933.39053
[3] Kadison, R.V.; Pedersen, G., Means and convex combinations of unitary operators, Math. scand., 57, 249-266, (1985) · Zbl 0573.46034
[4] Kadison, R.V.; Ringrose, J.R., Fundamentals of the theory of operator algebras, Elementary theory, (1983), Academic Press New York · Zbl 0518.46046
[5] Park, C., On the stability of the linear mapping in Banach modules, J. math. anal. appl., 275, 711-720, (2002) · Zbl 1021.46037
[6] Park, C., Modified Trif’s functional equations in Banach modules over a \(C\^{}\{∗\}\)-algebra and approximate algebra homomorphisms, J. math. anal. appl., 278, 93-108, (2003) · Zbl 1046.39022
[7] Park, C.; Park, W., On the Jensen’s equation in Banach modules, Taiwanese J. math., 6, 523-531, (2002) · Zbl 1035.39017
[8] Rassias, Th.M., On the stability of the linear mapping in Banach spaces, Proc. amer. math. soc., 72, 297-300, (1978) · Zbl 0398.47040
[9] Trif, T., On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions, J. math. anal. appl., 272, 604-616, (2002) · Zbl 1036.39021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.