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PurposeCognitive behavioral therapy (CBT) for depression had been found to be effective in reducing depressive and anxiety symptoms in breast cancer survivors. It is not known whether CBT for depression would also improve insomnia and quality of life (QOL). The aim of this study was to investigate whether CBT for depression would improve insomnia and QOL in a randomized controlled multicenter trial.Patients and methodsIn this study, breast cancer survivors (n=392) were randomly allocated to the following three groups: CBT (n=98), self-care management (SCM, n=98), and usual care (UC, n=196) in a ratio of 1:1:2. CBT and SCM received a series of nine sessions for 12 weeks, whereas UC received UC only. Insomnia and QOL were evaluated using Athens Insomnia Scale (AIS) and Functional Assessment of Cancer Therapy-Breast (FACT-B) questionnaire at baseline, 4, 12, and 24 weeks.ResultsThere was a significant intergroup difference in AIS and FACT-B scores (both P<0.01). CBT showed less insomnia problems and better overall QOL compared with those in SCM and UC (both P<0.01). No significant differences were found between SCM and UC in insomnia problems and overall QOL. Moreover, the effects of CBT on insomnia and QOL were maintained during the follow-up period.ConclusionCBT for depression can be effective in improving insomnia problems and QOL in the Chinese breast cancer survivors.

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LetB(H) be the algebra of all bounded linear operators on a complex Hilbert spaceHand 𝓐 ⊆B(H) be a von Neumann algebra with no central summands of typeI1. ForA,B∈ 𝓐, define byA∙B=AB+BA∗a new product ofAandB. In this article, it is proved that a map Φ: 𝓐 →B(H) satisfies Φ(A∙B∙C) = Φ(A) ∙B∙C+A∙ Φ(B) ∙C+A∙B∙Φ(C) for allA,B,C∈ 𝓐 if and only if Φ is an additive *-derivation.

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