Abstract
The following question concerning the computation of the norms of the tensor products of operators in the Lebesgue spaces is studied: Is it true that the norm of the tensor product A⊗B: Lp(μ⊗μ)→Lq(ν⊗ν) of operators A: Lp(μ)→Lq(ν) and B: Lp(μ)→Lq(ν) coincides with the product ‖A‖ ‖B‖ of their norms? An answer is positive if and only if 1≤p≤q≤+∞. Bibliography: 26 titles.
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