希尔伯特空间问题集

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作者: (美)哈尔莫斯著

出 版 社:

出版时间: 2009-4-1字数:版次: 1页数: 369印刷时间:开本: 16开印次: 1纸张:I S B N : 9787510004445包装: 平装目录

1. VECTORS

1. Limits of quadratic forms

2. Schwarz inequality

3. Representation of linear functionals

4. Strict convexity

5. Continuous curves

6. Uniqueness of crinkled arcs

7. Linear dimension

8. Total sets

9. Infinitely total sets

10. Infinite Vandermondes

11. T-total sets

12. Approximate bases

2. SPACES

13. Vector sums

14. Lattice of subspaces

15. Vector sums and the modular law

16. Local compactness and dimension

17. Separability and dimension

18. Measure in Hiibert space

3. WEAK TOPOLOGY

19. Weak closure of subspaces

20. Weak continuity of norm and inner product

21. Semicontinuity of norm

22. Weak separability

23. Weak compactness of the unit bali

24. Weak metrizabilitv of the unit ball

25. Weak closure of the unit sphere

26. Weak metrizability and separability

27. Uniform boundedness

28. Weak metrizability of Hilbert space

29. Linear functionals on /2

30. Weak completeness

4.ANALYTIC FUNCTIONS

31. Analytic Hilbert spaces

32. Basis for Ae

33. Real functions in He

34. Products in H2

35. Analytic characterization of H2

36. Functional Hilbcrt spaces

37. Kernel functions

38. Conjugation in functional Hilbert spaces

39. Continuity of extension

40. Radial limits

41. Bounded approximation

42. Multiplicativity of extension

43. Dirichlet problem

5. INFINITE MATRICES

44. Column-finite matrices

45. Schur test

46. Hilbert matrix

47. Exponential Hilbert matrix

48. Positivity of the Hilbert matrix

49. Series of vectors

6. BOUNDEDNESS AND INVERTIBILITY

50. Boundedness on bases

51. Uniform boundedness of linear transformations

52. lnvertible transformations

53. Diminishable complements

54. Dimension in inner-product spaces

55. Total orthonormal sets

56. Preservation of dimension

57. Projections of equal rank

58. Closed graph theorem

59. Range inclusion and factorization

60. Unbounded symmetric transformations

7.MULTIPLICATION OPERATORS

61. Diagonal operators

62. Multiplications on 12

63. Spectrum of a diagonal operator

64. Norm of a multiplication

……

 
 
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