Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지

작용소의 틈이론

  • 정일봉 (경북대학교 자연과학대학 수학과) ;
  • 이우영 (성균관대학교 자연과학부 수학과)
  • Published : 2001.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

복소힐버트 공간상에서 정의된 작용소 중에서 최근 많이 연구되는 분야는 부분정규작용소와 초정규작용소들 들 수 있다. 본 논문에서는 작용소의 부분정규성과 초정규성 사이에 있는 작용소의 여러 성질을 살펴보고 특히 $\textsc{k}$차초정규, 이차약초정규, 삼차약초정규, 다항초정규, 토에플리츠작용소 및 약부분정규작용소에 관한 최근의 연구 결과들을 살펴보며 이와 관련되 미해결 문제들을 제시한다. 마지막으로 틈이론의 응용으로서 작용소이론의 큰 문제인 불변공간문제와의 관련성을 살펴보고 틈이론의 전망과 기타 관련정보를 소개한다.

Keywords

References

  1. Duke Math. J. v.43 Subnormal Toeplitz operators and functions of bounded type M. B. Abrahamse
  2. J. Funct. Anal. v.38 An invariant subspace problem J. Agler
  3. Surveys of Some Recent Results in Operator Theory Ⅱ, Pitman Research Notes in Mathematics v.192 An abstract approach to model theory J. Agler
  4. Manuscripta Math. v.91 Subnormal operators with compact selfcommutator A. Aleman
  5. Integral Equations Operator Theory v.13 On p-hyponormal operators for 0
  6. Proc. Amer. Math. Soc. v.50 On quasinormal Toeplitz operators I. Amemiya;T. ITo;T. K. Wong
  7. Proc. Amer. Math. Soc. v.103 On joint hyponormality of operators A. Athavale
  8. Criteria for positively quadratically hyponormal weighted shifts J. Y. Bae;G. R. Exner;I. B. Jung
  9. Duke Math. J. v.22 Subnormal operators J. Bram
  10. Integral Equations Operator Theory v.1 Some invariant subspaces for subnormal operators S. Brown
  11. Ann. Math. v.125 Hyponormal operators with thick spectra have invariant subspaces S. Brown
  12. Bull. Korean Math. Soc. v.37 A propagation of quadratically hyponormal weighted shifts Y. B. Choi
  13. Math. Surveys amd Monographs, Amer. Math. Soc. v.36 The theory of subnormal operators J. B. Conway
  14. J. Reine Angew. Math. v.367 More subnormal Toeplitz operators C. Cowen
  15. Surveys of Some Recent Results in Operator Theory v.171 Hyponormal and subnormal Toeplitz operators J. B. Conway(ed.);B. B. Morrel(ed.)
  16. J. Reine Angew. Math. v.351 Some subnormal Toeplitz operators C. Cowen;J. Long
  17. Integral Equations Operator Theory v.13 Quadratically hyponormal weighted shifts R. E. Curto
  18. Proc. Symposia Pure Math. v.51 Joint hyponormality: A bridge between hyponormality and subnormality
  19. Proceedings of ELAM VⅡ, Reviata Union Mat. Arg. v.37 Polynomially hyponormal operators on Hilbert space
  20. Integral Equations Operator Theory v.17 Recursively generated weighted shifts and the subnormal completion problem, Ⅰ R. E. Curto;L. A. Fialkow
  21. Integral Equations Operator Theory v.17 Recursively generated weighted shifts and the subnormal completion problem, Ⅱ
  22. Memoirs Amer. Math. Soc. v.568 Solution of the truncated complex moment problem for flat data
  23. Memoirs Amer. Math. Soc. v.648 Flat extensions of positive moment matrices: recursively generated relations
  24. Integral Equations Operator Theory v.37 Quadratically hyponormal weighted shifts with two equal weights R. E. Curto;I. B. Jung
  25. Proc. Amer. Math. Soc. Extensions and extremality of recursively generated weighted shifts R. E. Curto;I. B. Jung;W. Y. Lee
  26. Subnormality and 2-hyponormality for Toeplitz operators R. E. Curto;S. H. Lee;W. Y. Lee
  27. Memoirs Amer. Math. Soc. Joint hyponormality of Toeplitz operators R. E. Curto;W. Y. Lee
  28. Flatness, perturbations and completions of weighted shifts
  29. Towards a model theory for 2-hyponormal operators
  30. Subnormality and k-hyponormality of Toeplitz operators
  31. Operator Th.: Adv. Appl. v.35 Hyponormal pairs of commuting operators R. E. Curto;P. Muhly;J. Xia
  32. Bull. Amer. Math. Soc. v.25 Existence of non-subnormal polynomially hyponormal operators R. E. Curto;M. Putinar
  33. J. Funct. Anal. v.115 Nearly subnormal operators and moment problems
  34. Integral Equations Operator Theory Model Theory for hyponormal contractions M. A. Dritschel;S. McCullough
  35. Proc. Amer. Math. Soc. v.92 A note on hyponormal weighted shifts P. Fan
  36. Summa Bras. Math. v.2 Normal dilations and extensions of operators P. R. Halmos
  37. Bull. Amer. Math. Soc. v.76 Ten problems in Hilbert space
  38. Integral Equations Operator Theory v.2 Ten years in Hilbert space
  39. A Hilbert space problem book
  40. Moment sequences and backward extensions of subnormal weighted shifts T. Hoover;I. B. Jung;A. Lambert
  41. Proc. Amer. Math. Soc. v.34 Subnormality and quasinormality of Toeplitz operators T. Ito;T. K. Wong
  42. Hankel and Toeplitz Matrices and Forms I. Iohvidov
  43. Integral Equations Operator Theory v.37 Aluthge transforms of operators I. B. Jung;E. I. Ko;C. M. Pearcy
  44. Integral Equations Operator Theory Spectral pictures of Aluthge transform of operators
  45. The iterated Aluthge transform of an operator
  46. Math. Japonica v.52 Backward extensions of hyponormal weighted shifts J. B. Jung;C. J. Lee
  47. Proc. Amer. Math. Soc. A formular for k-hyponormality of backstep extensions of subnormal weighted shifts
  48. Quartic moment problem I. B. Jung;C. J. Lee;S. H. Lee;W. Y. Lee
  49. Integral Equations Operator Theory v.36 Quadratically hyponormal weighted shifts and their examples I. B. Jung;S. S. Park
  50. J. Math. Anal. Appl. v.247 Cubically hyponormal weighted shifts and their examples
  51. Complex moment problem: matrix approach
  52. Adv. Math. v.127 Subnormal operators and quadrature domians J. E. MaCarthy;L. Yang
  53. Indiana Univ. Math. J. v.23 A decomposition of some operators B. B. Morrel
  54. Proc. Amer. Math. Soc. v.107 A note on joint hyponormality S. McCullough;V. Paulsen
  55. Trans. Amer. Math. Soc. Subnormal operators with finite rank self-commitator R. F. Olin;J. E. Thomson
  56. Proc. Amer. Math. Soc. v.125 Invariant subspaces for polynomially hyponormal operators B. Prunaru
  57. Math. Surveys v.13 Weighted shift operators and analytic function theory A. Shields
  58. Kexue Tongbao(English Ed.) v.28 Bergman shift is not unitarily equivalent to a Toeplitz operator S. Shunhua
  59. Adv. Math. v.127 Subnormal operators and quadrature domains J. E. McCarthy;L. Yang
  60. Mathematica Version 3.0 Wolfram Research
  61. Spectral theory of hyponormal operators D. Xia
  62. Integral Equations Operator Theory v.10 Analytic theory of subnormal Toeplitz operators
  63. Integral Equations Operator Theory v.24 On pure subnormal operators with finite rank self-commitators and related operator tuples