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The space of multipliers and convolutors of Orlicz spaces on a locally compact group

Hasan P. AghababaIbrahim AkbarbagluSaeid Maghsoudi — 2013

Studia Mathematica

Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let L φ ( G ) and L ψ ( G ) be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach L φ ( G ) -submodule X of L ψ ( G ) , the multiplier space H o m L φ ( G ) ( L φ ( G ) , X * ) is a dual Banach space with predual L φ ( G ) X : = s p a n ¯ u x : u L φ ( G ) , x X , where the closure is taken in the dual space of H o m L φ ( G ) ( L φ ( G ) , X * ) . We also prove that if φ is a Δ₂-regular N-function, then C v φ ( G ) , the space of convolutors of M φ ( G ) , is identified with the dual of a Banach algebra of functions on G under pointwise...

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