Algebras of holomorphic functions with Hadamard multiplication

• Autorzy: Hermann Render , Andreas Sauer
• Języki publikacji: EN

Abstrakty

EN

A systematic investigation of algebras of holomorphic functions endowed with the Hadamard product is given. For example we show that the set of all non-invertible elements is dense and that each multiplicative functional is continuous, answering some questions in the literature.

Słowa kluczowe

EN

Hadamard product; $B_0$-algebras; multiplicative functionals

Kategorie tematyczne

• 30A99: None of the above, but in this section
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 118
• Numer: 1
• Strony: 77-100

Daty

wydano

1996

otrzymano

1995-07-04

poprawiono

1995-09-07

Twórcy

autor

Hermann Render

• Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65 D-47057 Duisburg, Germany,

autor

Andreas Sauer

Bibliografia

• [1] S. Agmon, On the singularities of Taylor series with reciprocal coefficients, Pacific J. Math. 2 (1952), 431-453.
• [2] M. Akkar, M. El Azhari and M. Oudadess, Continuité des caractères dans les algèbres de Fréchet à bases, Canad. Math. Bull. 31 (1988), 168-174.
• [3] N. U. Arakelyan, On efficient analytic continuation of power series, Math. USSR-Sb. 52 (1985), 21-39.
• [4] E. Beckenstein, L. Narici and C. Suffel, Topological Algebras, North-Holland, Amsterdam, 1977.
• [5] R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954.
• [6] E. Borel, Sur les singularités des séries de Taylor, Bull. Soc. Math. France 26 (1898), 238-248.
• [7] R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210.
• [8] R. M. Brooks, A ring of analytic functions, II, ibid. 39 (1971), 199-208.
• [9] R. Brück and J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 294 (1992), 421-438.
• [10] R. Brück and J. Müller, Closed ideals in a convolution algebra of holomorphic functions, Canad. J. Math., to appear.
• [11] S. El-Helaly and T. Husain, Orthogonal bases are Schauder bases and a characterization of Φ-algebras, Pacific J. Math. 132 (1988), 265-275.
• [12] T. Husain and S. Watson, Topological algebras with orthogonal bases, ibid. 91 (1980), 339-347.
• [13] T. Husain and S. Watson, Algebras with unconditional orthogonal bases, Proc. Amer. Math. Soc. 79 (1980), 539-545.
• [14] B. Mitiagin, S. Rolewicz and W. Żelazko, Entire functions in $B_0$-algebras, Studia Math. 21 (1962), 291-306.
• [15] J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables Theory Appl. 18 (1992), 155-166.
• [16] P. K. Raševskiĭ [P. K. Rashevskiĭ], Closed ideals in a countably generated normed algebra of analytic entire functions, Soviet Math. Dokl. 6 (1965), 717-719.
• [17] R. Remmert, Funktionentheorie II, Springer, Berlin, 1991.
• [18] W. Żelazko, Banach Algebras, Elsevier, Amsterdam, 1973.
• [19] W. Żelazko, Metric generalizations of Banach algebras, Dissertationes Math. 47 (1965).