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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 \(S_p\).

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)
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