BMO spaces of σ-finite von Neumann algebras and Fourier–Schur multipliers on SUq(2)
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Abstract
We consider semigroup BMO spaces associated with an arbitrary σ-finite von Neumann algebra (M, ϕ). We prove that BMO always admits a predual, extending results from the finite case. Consequently, we can prove—in the current setting of BMO—that they are Banach spaces and they interpolate with Lp as in the commutative situation, namely [BMO(M), L◦p(M)]1/q ≈ L◦pq(M). We then study a new class of examples. We introduce the notion of Fourier–Schur multiplier on a compact quantum group and show that such multipliers naturally exist for SUq(2).