Around the discontinuity of the Riesz projection in the uniform metric
Abstract
The present paper is based on a lecture given by the author at the conference “Complex Analysis and Related Problems”, which was held from 29 June to July 4 in Kazan. The lecture was devoted to the Glicksberg conjecture and a related but independent assertion that the sums of certain ideals in a uniform algebra are never closed. This text contains several new formulations in comparison with the lecture and the existing literature.
About the Author
S. V. Kislyakov
Steklov Institute of Mathematics, St.Petersburg Department
Russian Federation
Russian Federation
27 Fontanka River Embankment, St. Petersburg 191023
References
1. W. Rudin, Projections on invariant subspaces, Proc. Amer. Math. Soc. 13 (3), 429–432 (1962). DOI: https://doi.org/10.2307/2034952
2. I. P. Natanson, Сonstructive theory of functions, GITTL, M–L, 1949.
3. I. Glicksberg, Some uncomplemented function algebras, Trans. Amer. Math. Soc. 111 (1), 121–137 (1964). DOI: https://doi.org/10.1090/S0002-9947-1964-0161175-8
4. S. V. Kislyakov, Proper uniform algebras are uncomplemented, Dokl. Math. 40 (3), 584– 586 (1990). URL: https://zbmath.org/?q=an:0729.46022
5. T. W. Gamelin, S. V. Kislyakov, Uniform algebras as Banach spaces, Handbook of the geometry of Banach spaces, V. 1, Elsevier Sci. B.V., 671–706 (2001). DOI: https://doi.org/10.1016/S1874-5849(01)80018-8
6. S. V. Kislyakov, I. K. Zlotnikov, Coinvariant subspaces of the shift operator and interpolation, Anal. Math. 44 (2), 219–236 (2018). DOI: https://doi.org/10.1007/s10476-018-0207-z
7. T. W. Gamelin, Uniform algebras, Prentice-Hall, N.J., 1969.
8. S. V. Kislyakov, “Uncomplemented uniform algebras”, Math. Notes 18 (1), 637–639 (1974). DOI: https://doi.org/10.1007/BF01461145
9. S. V. Kislyakov, “Uniform algebras as Banach spaces”, J. Math. Sci. 16 (3), 1102–1108 (1981). DOI: https://doi.org/10.1007/BF02427719
10. J. Diestel, H. Jarchow, A. Tonge, Absolutely summing operators, Cambridge Univ. Press, Cambridge, 1995. DOI: https://doi.org/10.1017/CBO9780511526138
Review
For citations:
Kislyakov S.V. Around the discontinuity of the Riesz projection in the uniform metric. Mathematics and Theoretical Computer Science. 2023;1(1):35-48. (In Russ.)
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