Normed Algebras

I Basic Ideas from Topology and Functional Analysis.- § 1. Linear spaces.- § 2. Topological spaces.- § 3. Topological linear spaces.- § 4. Normed spaces.- § 5. Hilbert space.- § 6. Integration on locally compact spaces.- II Fundamental Concepts and Propositions in the Theory of Normed Algebras.- § 7. Fundamental algebraic concepts.- § 8. Topological algebras.- § 9. Normed algebras.- § 10. Symmetric algebras.- III Commutative Normed Algebras.- § 11. Realization of a commutative normed algebra in the form of an algebra of functions.- § 12. Homomorphism and isomorphism of commutative algebras.- § 13. Algebra (or Shilov) boundary.- § 14. Completely symmetric commutative algebras.- § 15. Regular algebras.- § 16. Completely regular commutative algebras.- IV Representations of Symmetric Algebras.- § 17. Fundamental concepts and propositions in the theory of representations.- § 18. Embedding of a symmetric algebra in an algebra of operators.- § 19. Indecomposable functionals and irreducible representations.- § 20. Application to commutative symmetric algebras.- § 21. Generalized Schur lemma.- § 22. Some representations of the algebra $$/mathfrak{B}$$(?).- V Some Special Algebras.- § 23. Completely symmetric algebras.- § 24. Completely regular algebras.- § 25. Dual algebras.- § 26. Algebras of vector-valued functions.- VI Group Algebras.- § 27. Topological groups.- § 28. Definition and fundamental properties of a group algebra.- § 29. Unitary representations of a locally compact group and their relationship with the representations of the group algebra.- § 30. Positive definite functions.- § 31. Harmonic analysis on commutative locally compact groups.- § 32. Representations of compact groups.- VII Algebras of Operators in Hilbert Space.- § 33.Various topologies in the algebra $$/mathfrak{B}$$(?).- § 34. Weakly closed subalgebras of the algebra $$/mathfrak{B}$$(?).- § 35. Relative equivalence.- § 36. Relative dimension.- § 37. Relative trace.- § 38. Structure and examples of some types of factors.- § 39. Unitary algebras and algebras with trace.- VIII Decomposition of an Algebra of Operators into Irreducible Algebras.- § 40. Formulation of the problem; canonical form of a commutative algebra of operators in Hilbert space.- § 41. Direct integral of Hilbert spaces; the decomposition of an algebra of operators into the direct integral of irreducible algebras.- Appendix I Partially ordered sets and Zorn’s lemma.- Appendix II Borel spaces and Borel functions.- Appendix III Analytic sets.- Literature.