|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
S. C. Power
Title:
Hankel operators on Hilbert space
Additional book information:
Research Notes in Mathematics, No. 64, Pitman Advanced Publishing Program, Boston-London-Melbourne, 1982, 87 pp., $13.95. ISBN 0-273-08518-2
References:
- 1.
- V. M. Adamjan, D. Z. Arov and M. G. Krein, Infinite Hankel matrices and generalized Carathéodory-Fejér and Riesz problems, Funkcional Anal. i Prilozen 2 (1968), 1-19 = Functional Anal. Appl. 2 (1968), 1-18. MR 234274
- 2.
- V. M. Adamjan, D. Z. Arov and M. G. Krein, Analytic properties of Schmidt pairs for a Hankel operator and the generalized Shur-Takagi problem, Mat. Sb. 86 (128) (1971), 34-75 = Math. USSR Sbornik 15 (1971), 31-73. MR 298453
- 3.
- S. Axler, I. D. Berg, N. Jewell and A. Shields, Approximation by compact operators and the space H + C, Ann. of Math. (2) 109 (1979), 601-612. MR 534765
- 4.
- S. Axler, S.-Y. A. Chang and D. Sarason, Products of Toeplitz operators, J. Integral Equations Operator Theory 1 (1978), 285-309. MR 511973
- 5.
- C. Carathéodory and L. Fejér, Über den Zusammenhang der Extremen von harmonischen Funktionen mit ihren Koeffizienten und über den Picard-Landauschen Satz, Rend. Circ. Math. Palermo 32 (1911), 218-239.
- 6.
- D. N. Clark, On the spectra of bounded, Hermitian Hankel matrices, Amer. J. Math. 90 (1968), 627-656. MR 231112
- 7.
- D. N. Clark, On interpolating sequences and the theory of Hankel and Toeplitz operators, J. Functional Analysis 5 (1970), 247-258. MR 254628
- 8.
- L. A. Coburn, The C*-algebra generated by an isometry. II, Trans. Amer. Math. Soc. 137 (1969), 211-217. MR 236720
- 9.
- R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in L, Astérisque 77 (1980), 11-66. MR 604369
- 10.
- I. C. Goldberg and N. Ja. Krupnik, The algebra generated by Toeplitz matrices, Funkcional Anal. i Prilozen 3 (1969), 45-56. MR 250082
- 11.
- P. Hartman, On completely continuous Hankel matrices, Proc. Amer. Math. Soc. 9 (1958), 362-366. MR 108684
- 12.
- P. Hartman and A. Wintner, On the spectra of Toeplitz's matrices, Amer. J. Math. 72 (1950), 359-366. MR 36936
- 13.
- J. S. Howland, Trace class Hankel operators, Quart. J. Math. Oxford Ser. (2) 22 (1971), 147-159. MR 288630
- 14.
- M. G. Krein, Integral equations on a half line with difference kernel, Uspehi Mat. Nauk (N.S.) 13 (1958), No. 5 (83), 3-120. MR 102721
- 15.
- W. Magnus, On the spectrum of Hilbert's matrix, Amer. J. Math. 72 (1950), 699-704. MR 41358
- 16.
- Z. Nehari, On bounded bilinear forms, Ann. of Math. (2) 65 (1957), 153-162. MR 82945
- 17.
- V. V. Peller, Hankel operators of the class γ, Mat. Sb. (N.S.) 113 (155) (1980), 538-581. MR 602274
- 18.
- S. C. Power, The essential spectrum of a Hankel operator with piecewise continuous symbol, Michigan Math. J. 25 (1978), 117-121. MR 487567
- 19.
- S. C. Power, C*-algebra generated by Hankel operators and Toeplitz operators, J. Functional Analysis 31 (1979), 52-68. MR 523113
- 20.
- S. C. Power, Hankel operators with PQC symbol and singular integral operators, Proc. London Math. Soc. 40 (1980), 45-65. MR 579716
- 21.
- C. R. Putnam, Commutators and absolutely continuous operators, Trans. Amer. Math. Soc. 87 (1958), 513-525. MR 100226
- 22.
- M. Rosenblum, On the Hilbert matrix. I, II, Proc. Amer. Math. Soc. 9 (1958), 137-140; 9 (1958), 581-585. MR 94626
- 23.
- M. Rosenblum, The absolute continuity of Toeplitz's matrices, Pacific J. Math. 10 (1960), 987-996. MR 114125
- 24.
- T. Takagi, On an algebraic problem related to an analytic theorem of Carathéodory and Fejér and on an allied theorem of Landau, Japanese J. Math. 1 (1924), 83-93.
- 25.
- A. L. Volberg, Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang and D. Sarason, J. Operator Theory 7 (1982), 209-218. MR 658609
Additional Information:
Reviewer(s):
Douglas N.
Clark
Review Information:
Journal:
Bull. Amer. Math. Soc.
9
(1983),
98-102.
DOI:
10.1090/S0273-0979-1983-15171-6
PII:
S 0273-0979(1983)15171-6
|
