Book Review
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MathSciNet review:
1567943
Full text of review:
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This review is available free of charge.
Book Information:
Author:
H. Goldmann
Title:
Uniform Fréchet algebras
Additional book information:
North-Holland, Amsterdam, 1990, 355 pp., $102.50. ISBN 0-444-88488-2.
Richard Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455–471. MR 51445
Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 155016, DOI 10.2307/1970537
Andrew Browder, Introduction to function algebras, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0246125
R. M. Brooks, Partitions of unity in $F$-algebras, Math. Ann. 177 (1968), 265–272. MR 227773, DOI 10.1007/BF01350718
R. L. Carpenter, Continuity of derivations in $F$-algebras, Amer. J. Math. 93 (1971), 500–502. MR 287316, DOI 10.2307/2373390
Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
H. Goldmann, Finitely generated maximum modulus algebras, Ann. Polon. Math. 47 (1986), no. 2, 149–153. MR 884932, DOI 10.4064/ap-47-2-149-153
H. Goldmann, An analytic algebra without analytic structure in the spectrum, Ark. Mat. 27 (1989), no. 1, 89–95. MR 1004723, DOI 10.1007/BF02386361
Gerald M. Leibowitz, Lectures on complex function algebras, Scott, Foresman & Co., Glenview, Ill., 1970. MR 0428042
Ernest A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952), 79. MR 51444
Walter Rudin, Analyticity, and the maximum modulus principle, Duke Math. J. 20 (1953), 449–457. MR 56076
Zbigniew Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), no. 3, 363–386. MR 626955, DOI 10.1007/BF01679703
Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
John Wermer, Maximum modulus algebras and singularity sets, Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), no. 3-4, 327–331. MR 592560, DOI 10.1017/S0308210500012233
- [Ar] R. Arens, A generalization of normed rings, Pacific J. Math. 2 (1952), 455-471. MR 0051445
- [Bi] E. Bishop, Holomorphic completions, analytic continuations, and the interpolation of seminorms, Ann. of Math. (2) 78 (1963), 468-500. MR 155016
- [Br] A. Browder, Introduction to function algebras, Benjamin, New York, and Amsterdam, 1969. MR 246125
- [Bro] R. M. Brooks, Partitions of unity in F-algebras, Math. Ann. 177 (1968), 265-272. MR 227773
- [Ca] R. L. Carpenter, Continuity of derivations on F-algebras, Amer. J. Math. 93 (1971), 500-502. MR 287316
- [Ga] T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, NJ, 1969. MR 410387
- [Go1] H. Goldmann, Finitely generated maximum modulus algebras, Ann. Polon. Math. 47 (1986), 149-153. MR 884932
- [Go2] H. Goldmann, An analytic algebra without analytic structure in the spectrum, Ark. Math. 27 (1989), 89-95. MR 1004723
- [Le] G. M. Leibowitz, Lectures on complex function algebras, Scott, Foresman and Co., 1970. MR 428042
- [Mi] E. Michael, Locally m-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). MR 51444
- [Ru] W. Rudin, Analyticity and the maximum modulus principle, Duke Math. J. 20(1953), 449-457. MR 56076
- [S1] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. MR 626955
- [St] E. L. Stout, The theory of uniform algebras, Bogden & Quigley, Inc., New York, 1971. MR 423083
- [We] J. Wermer, Maximum modulus algebras and singularity sets, Proc. Roy. Soc. Edinburgh 86A (1980), 327-331. MR 592560
Review Information:
Reviewer:
John Wermer
Journal:
Bull. Amer. Math. Soc.
25 (1991), 180-184
DOI:
https://doi.org/10.1090/S0273-0979-1991-16059-3
