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We calculate the difference of one-loop vacuum energies for massive scalarfield in five-dimensional AdS black hole. (The same is done in five-dimensionaldeSitter space). In each case this difference is specified by the boundaryconditions corresponding to the double-trace operator (massive term) and itdescribes RG flow in the manner discussed by Gubser-Mitra for pure AdS space.For AdS black hole there occurs instability which is the manifestation of theHawking-Page phase transition. For stable phase of AdS black hole as well asfor deSitter bulk, c-function found beyond the leading order approximationshows the monotonic behaviour consistent with c-theorem.Comment: LaTeX file, 3 eps files, 26 pages. The discussion is clarified,  version to appear in PR

One-loop vacuum energy and RG flow induced by double-trace operators in AdS/CFT and dS/CFT correspondence