The Multiplier Problem.This work addresses primarily the task of characterizing multipliers. It is the characterization problem that is herein called the "multiplier problem." The meaningful presentation of this problem in the context of various topological algebras and linear spaces, and its investigation, makes up the content of the succeeding chapters. |
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A₁ algebra without order Banach space Clearly Closed Graph Theorem commutative Banach algebra commutes with translations compact Abelian group conclude Consequently continuous function continuous linear functional COROLLARY defines a continuous defines a linear defines a multiplier denote derived algebra element exists a unique fƐL G finite following are equivalent Fourier transform G is compact G is noncompact G₁ G₂ group and suppose H*-algebra Hence Hölder's inequality implies isometrically isomorphic L₁ G L₂ G Lemma Let G linear transformation locally compact Abelian Lp G Lp(G Lq(G M(Ap M(L G mapping maximal ideal maximal ideal space minimal approximate identity multiplicative linear functional norm algebra norm dense pseudomeasure quasimeasure regular maximal ideal self-adjoint semi-simple commutative Banach shows strong operator topology subalgebra subset subspace supremum norm supremum norm algebra TEM(A Theorem 98 Tx)y valid x(Ty Ар