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THE MULTIPLIERS FOR COMMUTATIVE HALGEBRAS
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algebra isomorphism algebra without order Banach space bounded linear operator characterization Clearly Closed Graph Theorem commutative Banach algebra commutes with translations compact Abelian group compact closure compact groups compact set conclude Consequently continuous function continuous linear functional COROLLARY defines a continuous defines a linear defines a multiplier denote derived algebra dual space element exists a unique f e CC(G finite following are equivalent Fourier transform G is compact G is noncompact group algebras group and suppose Hence implies isometrically isomorphic La(G Lemma Let G linear transformation Lj(G locally compact Abelian Lq(G Ls(G Lx G Lx(G M(L G maximal ideal space minimal approximate identity multiplicative linear functional norm dense Plancherel Theorem pseudomeasure quasimeasure regular maximal ideal semi-simple commutative Banach strong operator topology subalgebra subset subspace supremum norm algebra TeM(A Tf)A Tf*g Theorem 98 Tx)y valid vanishes weak x(Ty