General Theory of Banach Algebras

A₁ Akad Amer annihilator arbitrary assume B*-algebra Banach space bounded carrier space closed 2-sided ideal closed sets closed subalgebra closure commutative Banach algebra completely regular completes the proof complex numbers contains continuous functions COROLLARY defined definition denote dense direct sum divisor of zero Dokl dual equal equivalent exists follows functional F Furthermore Gelfand group algebra Hausdorff space hence hermitian element hermitian functional Hilbert space homomorphism idempotent identity element implies involution isometric isomorphism kernel left ideal Lemma linear functional locally compact mapping maximal modular minimal left ideal modular ideal modulo Nauk non-zero normed algebra obtain obviously open set operator algebras polynomials positive functional possess an identity preceding theorem primitive ideal Proc properties quasi-regular radical regular elements result right ideal scalar semi-simple Šilov Sp(x subalgebra subdirect sum subset theorem is proved Tôhoku Math topological divisor