Geodesic
An Analog of Wiener's Theorem for Infinite-Dimensional Banach Spaces
Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 191-202.

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In this paper, we study various generalizations of the classical Wiener algebra on a Banach space and prove analogs of Wiener's theorem on the invertibility of elements of such algebras.
Keywords: Wiener algebra, Banach space, Wiener's theorem, Fourier series, maximal ideal, Banach algebra
Mots-clés : convolution algebra, Aron–Berner extension. 
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A. V. Zagorodnjuk; M. A. Mitrofanov. An Analog of Wiener's Theorem for Infinite-Dimensional Banach Spaces. Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 191-202. http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a2/

[1] T. Gamelin, Ravnomernye algebry, Mir, M., 1973 | MR | Zbl

[2] A. S. Nemirovskii, “Ob odnoi tsepochke algebr na gilbertovom share”, Funkts. analiz i ego pril., 5:1 (1971), 85–86 | MR | Zbl

[3] A. S. Nemirovskii, S. M. Semenov, “O polinomialnoi approksimatsii funktsii na gilbertovom prostranstve”, Matem. sb., 92:2 (1973), 257–281 | MR | Zbl

[4] R. M. Aron, B. J. Cole, T. W. Gamelin, “Spectra of algebras of analytic functions on a Banach space”, J. Reine Angew. Math., 415 (1991), 51–93 | MR | Zbl

[5] A. Zagorodnyuk, “Spectra of algebras of analytic functions and polynomials on Banach spaces”, Function spaces, Contemp. Math., 435, Amer. Math. Soc., Providence, RI, 2007, 381–394 | MR | Zbl

[6] S. Dineen, “Holomorphy types on a Banach space”, Studia Math., 34 (1971), 241–288 | MR | Zbl

[7] K. Floret, “Natural norms on symmetric tensor products of normed spaces”, Note Mat., 17 (1997), 153–188 | MR | Zbl

[8] J. Mujica, Complex Analysis in Banach Spaces. Holomorphic Functions and Domains of Holomorphy in Finite and Infinite Dimensions, North-Holland Math. Stud., 120, North-Holland Publ., Amsterdam, 1986 | MR | Zbl

[9] S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monogr. Math., Springer-Verlag, Berlin, 1999 | MR | Zbl

[10] S. Dineen, Complex Analysis in Locally Convex Spaces, Math. Stud., 57, North-Holland Publ., Amsterdam, 1981 | MR | Zbl

[11] U. Rudin, Funktsionalnyi analiz, Mir, M., 1975 | MR | Zbl

[12] R. H. Cameron, “Analytic functions of absolutely convergent generalized trigonometric sums”, Duke Math. J., 3:4 (1937), 682–688 | DOI | MR | Zbl

[13] R. Arens, I. M. Singer, “Generalized analytic functions”, Trans. Amer. Math. Soc., 81:2 (1956), 379–393 | DOI | MR | Zbl

[14] M. A. Naimark, Normirovannye koltsa, GITTL, M., 1956 | MR | Zbl

[15] M. A. Mitrofanov, “Approksimatsiya nepreryvnykh funktsii na kompleksnykh banakhovykh prostranstvakh”, Matem. zametki, 86:4 (2009), 557–570 | DOI | MR | Zbl

[16] A. Zagorodnyuk, “Spectra of algebras of entire functions on Banach spaces”, Proc. Amer. Math. Soc., 134:9 (2006), 2559–2569 | DOI | MR | Zbl