Book Review
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MathSciNet review:
1567922
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Book Information:
Authors:
M. Martin and
M. Putinar
Title:
Lectures on hyponormal operators
Additional book information:
Birkhauser, Boston, 1989, 305 pp., $80.00. ISBN 3-7643-2329-9.
C. A. Berger and B. I. Shaw, Selfcommutators of multicyclic hyponormal operators are always trace class, Bull. Amer. Math. Soc. 79 (1973), 1193–1199, (1974). MR 374972, DOI 10.1090/S0002-9904-1973-13375-0
C. A. Berger and B. I. Shaw, Intertwining, analytic structure, and the trace norm estimate, Proceedings of a Conference on Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Lecture Notes in Math., Vol. 345, Springer, Berlin, 1973, pp. 1–6. MR 0361885
Arne Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1948), 239–255. MR 27954, DOI 10.1007/BF02395019
Scott W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), no. 3, 310–333. MR 511974, DOI 10.1007/BF01682842
Scott W. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. of Math. (2) 125 (1987), no. 1, 93–103. MR 873378, DOI 10.2307/1971289
Richard W. Carey and Joel D. Pincus, Commutators, symbols, and determining functions, J. Functional Analysis 19 (1975), 50–80. MR 0442743, DOI 10.1016/0022-1236(75)90006-3
Richard W. Carey and Joel D. Pincus, Mosaics, principal functions, and mean motion in von Neumann algebras, Acta Math. 138 (1977), no. 3-4, 153–218. MR 435901, DOI 10.1007/BF02392315
Richard W. Carey and Joel D. Pincus, Principal functions, index theory, geometric measure theory and function algebras, Integral Equations Operator Theory 2 (1979), no. 4, 441–483. MR 555774, DOI 10.1007/BF01691073
Richard W. Carey and Joel D. Pincus, An integrality theorem for subnormal operators, Integral Equations Operator Theory 4 (1981), no. 1, 10–44. MR 602618, DOI 10.1007/BF01682745
John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
Paul R. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), 125–134. MR 44036
12. P. R. Halmos, Introduction to Hilbert space, Chelsea, New York, 1957.
J. William Helton and Roger E. Howe, Integral operators: commutators, traces, index and homology, Proceedings of a Conference Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Lecture Notes in Math., Vol. 345, Springer, Berlin, 1973, pp. 141–209. MR 0390829
Tosio Kato, Smooth operators and commutators, Studia Math. 31 (1968), 535–546. MR 234314, DOI 10.4064/sm-31-5-535-546
Joel David Pincus, Commutators and systems of singular integral equations. I, Acta Math. 121 (1968), 219–249. MR 240680, DOI 10.1007/BF02391914
Mihai Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385–395. MR 757441
C. R. Putnam, On the structure of semi-normal operators, Bull. Amer. Math. Soc. 69 (1963), 818–819. MR 166613, DOI 10.1090/S0002-9904-1963-11048-4
C. R. Putnam, An inequality for the area of hyponormal spectra, Math. Z. 116 (1970), 323–330. MR 270193, DOI 10.1007/BF01111839
Marvin Rosenblum, A spectral theory for self-adjoint singular integral operators, Amer. J. Math. 88 (1966), 314–328. MR 198294, DOI 10.2307/2373195
James E. Thomson, Invariant subspaces for algebras of subnormal operators, Proc. Amer. Math. Soc. 96 (1986), no. 3, 462–464. MR 822440, DOI 10.1090/S0002-9939-1986-0822440-1
Dao Xing Xia, Non-normal operators. II, Acta Math. Sinica 21 (1978), no. 2, 187–189 (Chinese). MR 507200
Dao Xing Xia, Non-normal operators. II, Acta Math. Sinica 21 (1978), no. 2, 187–189 (Chinese). MR 507200
Daoxing Xia, The analytic model of a subnormal operator, Integral Equations Operator Theory 10 (1987), no. 2, 258–289. MR 878248, DOI 10.1007/BF01199080
Daoxing Xia, Analytic theory of subnormal operators, Integral Equations Operator Theory 10 (1987), no. 6, 880–903. MR 911997, DOI 10.1007/BF01196125
- 1.
- C. A. Berger and B. I. Shaw, Selfcommutators of multicyclic hyponormal operators are trace class, Bull. Amer. Math. Soc. (N.S.) 79 (1973), 1193-1199. MR 0374972
- 2.
- C. A. Berger and B. I. Shaw, Intertwining, analytic structure, and the trace norm estimate, Proc. Conf. Operator Theory, Lecture Notes in Math., vol. 345, Springer-Verlag, Berlin, 1973, pp. 1-6. MR 361885
- 3.
- A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. MR 27954
- 4.
- S. W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), 310-333. MR 511974
- 5.
- S. W. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. of Math. 125 (1987), 93-103. MR 873378
- 6.
- R. W. Carey and J. D. Pincus, Commutators, symbols, and determining functions, J. Funct. Anal. 19 (1975), 50-80. MR 442743
- 7.
- R. W. Carey and J. D. Pincus, Mosaics, principal functions, and mean motion in von Neumann algebras, Acta Math. 138 (1977), 153-218. MR 435901
- 8.
- R. W. Carey and J. D. Pincus, Principal functions, index theory, geometric theory and function algebras, Integral Equations Operator Theory 2 (1979), 441-483. MR 555774
- 9.
- R. W. Carey and J. D. Pincus, An integrality theorem for subnormal operators, Integral Equations Operator Theory 4 (1981), 10-44. MR 602618
- 10.
- J. B. Conway, A course in functional analysis, 2nd ed., Springer-Verlag, New York, 1990. MR 1070713
- 11.
- P. R. Halmos, Normal dilations and extensions of operators, Summa Bras. Math. 2 (1950), 125-134. MR 44036
- 12.
- P. R. Halmos, Introduction to Hilbert space, Chelsea, New York, 1957.
- 13.
- J. W. Helton and R. Howe, Integral operators, commutator traces, index and homology, in Proc. Conf. Operator Theory, Lecture Notes in Math., vol. 345, Springer-Verlag, Berlin, 1973. MR 390829
- 14.
- T. Kato, Smooth operators and commutators, Studia Math. 31 (1968), 535-546. MR 234314
- 15.
- J. D. Pincus, Commutators and systems of singular integral equations, I, Acta Math. 121 (1968), 219-249. MR 240680
- 16.
- M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), 385-393. MR 757441
- 17.
- C. R. Putnam, On the structure of semi-normal operators, Bull. Amer. Math. Soc. (N.S.) 69 (1963), 818-819. MR 166613
- 18.
- C. R. Putnam, An inequality for the area of hyponormal spectra, Math Z. 116 (1970), 323-330. MR 270193
- 19.
- M. Rosenblum, A spectral theorem for selfadjoint singular operators, Amer. J. Math. 88 (1966), 314-328. MR 198294
- 20.
- J. E. Thomson, Invariant subspaces for algebras of subnormal operators, Proc. Amer. Math. Soc. 96 (1986), 462-464. MR 822440
- 21.
- D. Xia, On non-normal operators, I, Chinese J. Math. 3 (1963), 232-246. MR 507200
- 22.
- D. Xia, On non-normal operators, II, Acta Math. Sinica 21 (1978), 187-189. MR 507200
- 23.
- D. Xia, The analytic model of a subnormal operator, Integral Equations Operator Theory 10 (1987), 258-289. MR 878248
- 24.
- D. Xia, Analytic theory of subnormal operators, Integral Equations Operator Theory 10 (1987), 880-903. MR 911997
Review Information:
Reviewer:
John B. Conway
Journal:
Bull. Amer. Math. Soc.
24 (1991), 441-447
DOI:
https://doi.org/10.1090/S0273-0979-1991-16062-3