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Book Review
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Book Information
Author(s):
A. B\"ottcher and B. Silbermann
Title:
Analysis of Toeplitz operators
Additional book information:
Springer-Verlag, New York, 1990, 512 pp., US$79.00. ISBN 3-540-52147-X
References:
- [1]
- M. B. Abrahamse, Subnormal Toeplitz operators and functions of bounded type, Duke J. Math. \textbf{43} (1976), 597--604.
- [2]
- M. B. Abrahamse, The spectrum of a Toeplitz operator with multiplicatively periodic symbol, J. Funct. Anal. \textbf{31} (1979), 224--233.
- [3]
- S. Axler, S.-Y. A. Chang, and D. Sarason, Products of Toeplitz operators, Integral Equations Operator Theory \textbf{1} (1978), 285--309.
- [4]
- C. Berger and L. Coburn, Toeplitz operators and quantum mechanics, J. Funct. Anal. \textbf{68} (1986), 273--299.
- [5]
- A. B\"ottcher and B. Silbermann, Invertibility and asymptotics of Toeplitz matrices, Akademie-Verlag, Berlin, 1983.
- [6]
- A. Brown and P. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. \textbf{213} (1963), 89--102.
- [7]
- D. Clark, On Toeplitz operators with loops. {\rm II}, J. Operator Theory \textbf{7} (1982), 109--123.
- [8]
- D. Clark and J. Morrel, On Toeplitz operators and similarity, Amer. J. Math. \textbf{100} (1978), 973--986.
- [9]
- L. Coburn, The $C^*$-algebra generated by an isometry. {\rm II}, Trans. Amer. Math. Soc. \textbf{137} (1969), 211--217.
- [10]
- L. Coburn and R. Douglas, Translation operators on a half-line, Proc. Nat. Acad. Sci. U.S.A. \textbf{62} (1969), 1010--1013.
- [11]
- J. Conway, \emph{The theory of subnormal operators}, Amer. Math. Soc., Providence, RI, 1991.
- [12]
- C. Cowen and J. Long, Some subnormal Toeplitz operators, J. Reine Angew. Math. \textbf{351} (1984), 216--220.
- [13]
- A. Devinatz, Toeplitz operators on $H^2$ spaces, Trans. Amer. Math. Soc. \textbf{112} (1964), 304--317.
- [14]
- R. Douglas, \emph{Another look at real-valued index theory}, vol. II (J. Conway and B. Morrel, eds.), Pitman Res. Notes Math. Ser., Longman Sci. Tech., Essex, UK, (co-published with Wiley, New York), pp. 91--120.
- [15]
- R. Douglas, Local Toeplitz operators, Proc. London Math. Soc. (3) \textbf{36} (1978), 243--272.
- [16]
- R. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972.
- [17]
- I. Gohberg, On Toeplitz matrices constituted by the Fourier coefficients of piecewise continuous functions, Funktsional. Anal. i Prilozhen. \textbf{1} (1967), 91--92.
- [18]
- I. Gohberg and M. Kre\u \i n, Systems of integral equations on a half-line with kernels depending on the difference of arguments, Uspekhi Mat. Nauk \textbf{13} (1958), 3--72.
- [19]
- P. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. \textbf{76} (1970), 887--933.
- [20]
- P. Hartman and A. Wintner, On the spectra of Toeplitz matrices, Amer. J. Math. \textbf{72} (1950), 359--366.
- [21]
- P. Hartman and A. Wintner, The spectra of Toeplitz matrices, Amer. J. Math. \textbf{76} (1954), 867--882.
- [22]
- R. Ismagilov, The spectrum of Toeplitz matrices, Dokl. Akad. Nauk SSSR \textbf{149} (1963), 769--772.
- [23]
- J. Kaminker, \emph{Operator algebraic invariants for elliptic operators}, Proc. Sympos. Pure Math., vol. 51, Part 1, Amer. Math. Soc., Providence, RI, 1990 pp.~307--314.
- [24]
- N. K. Nikol\cprime skii, Treatise on the shift operator, ``Nauka'', Moscow, 1980 (Russian).
- [25]
- V. Peller, \emph{Hankel operators and multivariate stationary processes}, Proc. Sympos. Pure Math., vol. 51, Part 1, Amer. Math. Soc., Providence, RI, 1990 pp.~357--371.
- [26]
- S. Power, Essential spectra of piecewise continuous Fourier integral operators, Proc. Royal Irish Acad. Sect. A \textbf{18} (1981), 1--7.
- [27]
- S. Power, \emph{Hankel operators on Hilbert space}, Pitman Advanced Publishing Program, Boston, London, and Melbourne, 1982.
- [28]
- M. Rosenblum, A concrete spectral theory for self-adjoint Toeplitz operators, Amer. J. Math. \textbf{87} (1965), 709--718.
- [29]
- M. Rosenblum, The absolute continuity of Toeplitz matrices, Pacific J. Math. \textbf{10} (1960), 987--996.
- [30]
- M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford Univ. Press, New York and Oxford, 1985.
- [31]
- D. Sarason, Toeplitz operators with piecewise quasicontinuous symbols, Indiana Univ. Math. J. \textbf{26} (1977), 817--838.
- [32]
- B. Silbermann, The $C^*$-algebra generated by Toeplitz and Hankel operators with piecewise quasicontinuous symbols, Integral Equations Operator Theory \textbf{10} (1987), 730--738.
- [33]
- I. Simonenko, The Riemann boundary value problem with measurable coefficients, Dokl. Akad. Nauk SSSR \textbf{135} (1960), 538--541.
- [34]
- Sun Shunhua, Bergman shift is not unitarily equivalent to a Toeplitz operator, Kexue Tongbao \textbf{28} (1983), 1027--1030.
- [35]
- H. Upmeier, \emph{Toeplitz operators and index theory in several complex variables}, Proc. Sympos. Pure Math., vol. 51, Part 1, Amer. Math. Soc., Providence, RI, 1990 pp.~585--598.
- [36]
- A. Vol\cprime berg, Two remarks concerning the theorem of\, S. Axler, S.-Y. A. Chang and D. Sarason, J. Operator Theory \textbf{7} (1982), 209--218.
- [37]
- H. Widom, Inversion of Toeplitz matrices. {\rm II}, Illinois J. Math. \textbf{4} (1960), 88--99.
- [38]
- H. Widom, Inversion of Toeplitz matrices. {\rm III}, Notices Amer. Math. Soc. \textbf{7} (1960), 63.
- [39]
- H. Widom, On the spectrum of Toeplitz operators, Pacific J. Math. \textbf{14} (1964), 365--375.
- [40]
- K. Zhu, \emph{Operator theory on function spaces}, Marcel Dekker, New York, 1990.
Additional Information:
Reviewer(s):
Thomas
Kriete
Review Information:
Journal:
Bull. Amer. Math. Soc.
28
(1993),
387-396.
DOI:
10.1090/S0273-0979-1993-00370-7
PII:
S 0273-0979(1993)00370-7
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