Automatic continuity of multiplicative polynomial
operators on Banach algebras

A.V. Zagorodnyuk

In this paper we prove the continuity of multiplicative polynomial operators from a complex Banach algebra with unit to a complex uniform Banach algebra.

1. J. Bochnak, J. Siciak Polynomials and multilinear mappings in topological vector space // Studia Math. V. 39 – 1971 p. 59–76

2. J. Cusak Automatic continuity and topologically simple radical Banach algebras // J. London Math. Soc. (2) V. 16 – 1977 p. 493–500

3. H.G. Dales Automatic continuity: a survey // Bull. London Math. Soc. V. 10 – 1978 p. 129–183

4. L.M. Drużkowski Two criteria for continuity of polynomials and $G$-holomorphic mappings in infinite dimensions // Univ. Iagel. Acta Math. V. 24 -- 1984 p. 135-138

5. C.S. Fernandez The closed graph theorem for multilinear mappings // J. Math. and Math. Sci. Internat. V. 19 № 2 – 1996 p. 407–408

6. Z. Gajda Christensen measurability of polynomial functions and convex functions of higher order // Annales Polon. Math. V. 47 – 1986 p. 25–40

7. T.W. Gamelin Uniform Algebras , Prentice-Hall, Inc. ,addr Englewood Cliffs, N.J. – 1969, 335 p

8. A. Plichko and A. Zagorodnyuk On automatic continuity and three problems of “The Scottish Book" concerning the boundedness of polynomial functionals // submitted to “J. of Math. Anal. and Appl."

	Automatic continuity of multiplicative polynomial operators on Banach algebras
Author	A.V. Zagorodnyuk Institute of Applied Problems of Mechanics and Mathematics,str. Naukova 3b, Lviv, 290053, Ukraine
Abstract	In this paper we prove the continuity of multiplicative polynomial operators from a complex Banach algebra with unit to a complex uniform Banach algebra.
Keywords	multiplicative polynomial operators, complex Banach algebra with unit, complex uniform Banach algebra
DOI	doi:10.30970/ms.12.2.205-207
Reference	1. J. Bochnak, J. Siciak Polynomials and multilinear mappings in topological vector space // Studia Math. V. 39 – 1971 p. 59–76 2. J. Cusak Automatic continuity and topologically simple radical Banach algebras // J. London Math. Soc. (2) V. 16 – 1977 p. 493–500 3. H.G. Dales Automatic continuity: a survey // Bull. London Math. Soc. V. 10 – 1978 p. 129–183 4. L.M. Drużkowski Two criteria for continuity of polynomials and $G$-holomorphic mappings in infinite dimensions // Univ. Iagel. Acta Math. V. 24 -- 1984 p. 135-138 5. C.S. Fernandez The closed graph theorem for multilinear mappings // J. Math. and Math. Sci. Internat. V. 19 № 2 – 1996 p. 407–408 6. Z. Gajda Christensen measurability of polynomial functions and convex functions of higher order // Annales Polon. Math. V. 47 – 1986 p. 25–40 7. T.W. Gamelin Uniform Algebras , Prentice-Hall, Inc. ,addr Englewood Cliffs, N.J. – 1969, 335 p 8. A. Plichko and A. Zagorodnyuk On automatic continuity and three problems of “The Scottish Book" concerning the boundedness of polynomial functionals // submitted to “J. of Math. Anal. and Appl."
Pages	205-207
Volume	12
Issue	2
Year	1999
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Automatic continuity of multiplicative polynomial operators on Banach algebras