AMS Chelsea Publishing 1957; 114 pp; hardcover Volume: 82 Reprint/Revision History: second AMS printing 2000 ISBN10: 0821813781 ISBN13: 9780821813782 List Price: US$23 Member Price: US$20.70 Order Code: CHEL/82.H
 A clear, readable introductory treatment of Hilbert Space. The multiplicity theory of continuous spectra is treated, for the first time in English, in full generality. Reviews "The main purpose of this book is to present the socalled multiplicity theory and the theory of unitary equivalence, for arbitrary spectral measures, in separable or not separable Hilbert space ... The approach to this theory, as presented by the author, has much claim to novelty. By a skillful permutation of the fundamental ideas of Wecken and Nakano and consistently referring to the simple situation in the finitedimensional case, the author succeeds in presenting the theory in a clear and perspicuous form."  Mathematical Reviews Table of Contents The Geometry of Hilbert Space  1. Linear functionals
 2. Bilinear functionals
 3. Quadratic forms
 4. Inner product and norm
 5. The inequalities of Bessel and Schwarz
 6. Hilbert space
 7. Infinite sums
 8. Conditions for summability
 9. Examples of Hilbert space
 10. Subspaces
 11. Vectors in and out of subspaces
 12. Orthogonal complements
 13. Vector sums
 14. Bases
 15. A nonclosed vector sum
 16. Dimension
 17. Boundedness
 18. Bounded bilinear functionals
The Algebra of Operators  19. Operators
 20. Examples of operators
 21. Inverses
 22. Adjoints
 23. Invariance
 24. Hermitian operators
 25. Normal and unitary operators
 26. Projections
 27. Projections and subspaces
 28. Sums of projections
 29. Products and differences of projections
 30. Infima and suprema of projections
 31. The spectrum of an operator
 32. Compactness of spectra
 33. Transforms of spectra
 34. The spectrum of a Hermitian operator
 35. Spectral Heuristics
 36. Spectral measures
 37. Spectral integrals
 38. Regular spectral measures
 39. Real and complex spectral measures
 40. Complex spectral integrals
 41. Description of the spectral subspaces
 42. Characterization of the spectral subspaces
 43. The spectral theorem for Hermitian operators
 44. The spectral theorem for normal operators
The Analysis of Spectral Measures  45. The Problem of unitary equivalence
 46. Multiplicity functions in finitedimensional spaces
 47. Measures
 48. Boolean operations on measures
 49. Multiplicity functions
 50. The canonical example of a spectral measure
 51. Finitedimensional spectral measures
 52. simple finitedimensional spectral measures
 53. The commutator of a set of projections
 54. Pairs of commutators
 55. Columns
 56. Rows
 57. Cycles
 58. Separable projections
 59. Characterizations of rows
 60. Cycles and rows
 61. The existence of rows
 62. Orthogonal systems
 63. The power of a maximal orthogonal system
 64. Multiplicities
 65. Measures from vectors
 66. Subspaces from measures
 67. The multiplicity function of a spectral measure
 69. Conclusion
 References
 Bibliography
