Aleksandrov, A. B. Toeplitz-Schur multipliers of the class \(S_p(L^2(G))\) for \(p< 1\). (English. Russian original) Zbl 1067.43002 J. Math. Sci., New York 120, No. 5, 1645-1652 (2004); translation from Zap. Nauchn. Semin. POMI 282, 5-19 (2001). Summary: We study Toeplitz-Schur multipliers of the Schatten-von Neumann class \(S_p\) for \(0< p< 1\). We describe all functions \(F\) on an arbitrary commutative locally compact group \(G\) satisfying the following condition: for any integral operator in \(S_p\) with kernel function \(k(x,y)\), the kernel function \(F(x-y)k(x)k(y)\) defines also an integral operator in \(S_p\). Cited in 1 Document MSC: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) 47B38 Linear operators on function spaces (general) × Cite Format Result Cite Review PDF Full Text: DOI