An Introduction to Abstract Harmonic Analysis

adverse application assumed Banach algebra Banach space bounded called Chapter character choose clearly closed closure commutative complex numbers complex-valued condition considered contains continuous function converges Corollary correspondence defined definition dense direct element equal equivalent exists extended fact field finite follows function ƒ given Hausdorff space hence Hilbert space homomorphism hull identity implies includes inequality integral intersection invariant inverse isomorphic Lemma limit linear linear functional locally compact mapping measure minimal multiplication neighborhood norm normed linear space null open set operator ordered orthogonal particular positive Proof proper proving regular maximal ideal remark representation respect self-adjoint sequence spectrum sphere subset subspace summable suppose theorem theory tion topology transformation uniform uniformly unique vanish weak topology whole zero