Seminar on Banach algebras (Q1713002)

These are lecture notes of a seminar on algebraic methods in functional analysis, held in Brussels in 1962/63 by one of the leading geometers of the last century. The headings of the ten sections give an impression of the contents: (1) Banach spaces and algebras; (2) Algebras with continuous inverses; (3) Commutative algebras with continuous inverses; (4) Banach algebras with involution; (5) Spectrum and operational calculus; (6) Unitary representations of algebras with involution; (7) Irreducible unitary representations of algebras with involution; (8) Unitary representations of complete algebras with continuous inverse; (9) Representation of positive functionals; (10) Representation of groups and group algebras. In some aspects, the text follows the classical book by \textit{M. A. Naĭmark} [Normed rings. Groningen: P. Noordhoff (1959; Zbl 0089.10102)]. It might be of historical interest for specialists in the field.