Author | Naimark, M. A. author |
---|---|
Title | Normed Algebras [electronic resource] / by M. A. Naimark |
Imprint | Dordrecht : Springer Netherlands, 1972 |
Connect to | http://dx.doi.org/10.1007/978-94-009-9260-3 |
Descript | XVI, 600 p. online resource |
I Basic Ideas from Topology and Functional Analysis -- ยง 1. Linear spaces -- ยง 2. Topological spaces -- ยง 3. Topological linear spaces -- ยง 4. Normed spaces -- ยง 5. Hilbert space -- ยง 6. Integration on locally compact spaces -- II Fundamental Concepts and Propositions in the Theory of Normed Algebras -- ยง 7. Fundamental algebraic concepts -- ยง 8. Topological algebras -- ยง 9. Normed algebras -- ยง 10. Symmetric algebras -- III Commutative Normed Algebras -- ยง 11. Realization of a commutative normed algebra in the form of an algebra of functions -- ยง 12. Homomorphism and isomorphism of commutative algebras -- ยง 13. Algebra (or Shilov) boundary -- ยง 14. Completely symmetric commutative algebras -- ยง 15. Regular algebras -- ยง 16. Completely regular commutative algebras -- IV Representations of Symmetric Algebras -- ยง 17. Fundamental concepts and propositions in the theory of representations -- ยง 18. Embedding of a symmetric algebra in an algebra of operators -- ยง 19. Indecomposable functionals and irreducible representations -- ยง 20. Application to commutative symmetric algebras -- ยง 21. Generalized Schur lemma -- ยง 22. Some representations of the algebra $$\mathfrak{B}$$(?) -- V Some Special Algebras -- ยง 23. Completely symmetric algebras -- ยง 24. Completely regular algebras -- ยง 25. Dual algebras -- ยง 26. Algebras of vector-valued functions -- VI Group Algebras -- ยง 27. Topological groups -- ยง 28. Definition and fundamental properties of a group algebra -- ยง 29. Unitary representations of a locally compact group and their relationship with the representations of the group algebra -- ยง 30. Positive definite functions -- ยง 31. Harmonic analysis on commutative locally compact groups -- ยง 32. Representations of compact groups -- VII Algebras of Operators in Hilbert Space -- ยง 33. Various topologies in the algebra $$\mathfrak{B}$$(?) -- ยง 34. Weakly closed subalgebras of the algebra $$\mathfrak{B}$$(?) -- ยง 35. Relative equivalence -- ยง 36. Relative dimension -- ยง 37. Relative trace -- ยง 38. Structure and examples of some types of factors -- ยง 39. Unitary algebras and algebras with trace -- VIII Decomposition of an Algebra of Operators into Irreducible Algebras -- ยง 40. Formulation of the problem; canonical form of a commutative algebra of operators in Hilbert space -- ยง 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 Zornโs lemma -- Appendix II Borel spaces and Borel functions -- Appendix III Analytic sets -- Literature