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A characterization of real Hilbert spaces using the Bochnak complexification norm.


Ferrera Cuesta, Juan and Muñoz-Fernández, Gustavo A. (2003) A characterization of real Hilbert spaces using the Bochnak complexification norm. Archiv der Mathematik, 80 ( 4). pp. 384-392. ISSN 0003-889X

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In this paper we find an alternative description of the Bochnak complexification of a real Hilbert space. This new interpretation of the Bochnak norm lets us give a characterization of a real inner product space.

Item Type:Article
Uncontrolled Keywords:Banach-Spaces; Multilinear maps; Polynomials
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:15224

C. BENITEZ and Y. SARANTOPOULOS and A. TONGE, Lower bounds for norms of products of polynomials. Math. Proc. Cambridge Philos. Soc. 124, 395–408 (1998).

J. BOCHNAK, Analytic functions in Banach spaces. Studia Math. 35, 273–292 (1970).

J. BOCHNAK and J. SICIAK, Polynomials and multilinear mappings in topological vector spaces. Studia Math. 39, 59–76 (1971).

A. DEFANT and K. FLORET, Tensor norms and operator ideals. North Holland. Math. Stud. 176 (1993).

P. KIRWAN, Complexifications of multilinear and polynomial mappings. Ph. D. thesis, National University of Ireland, Galway 1997.

J. LINDENSTRAUSS and L. ZTAFRIRI, Classical Banach spaces I. Ergeb. Math. Grenzgeb. 92, Berlin-Heidelberg-New York 1977.

G. A. MU~NOZ, Two Problems on Real Banach Spaces: Complexifications and Bernstein-Markov Type Inequalities. Ph.D. thesis, Universidad Complutense de Madrid, Spain. 1999.

G. A. MU~NOZ, Complexifications of polynomials and multilinear maps on real Banach spaces. In: Function Spaces, The Fifth Conference, Poznan 1998 H. Hudzik and L. Skrzypczak, eds., Lecture Notes Pure Appl. Math. 213, 389–406, New York, 2000.

G. A. MU~NOZ, Y. SARANTOPOULOS and A. TONGE, Complexifications of real Banach spaces, polynomials and multilinear maps. Studia Math. 134, 1–33 (1999).

A. D. MICHAL and M. WYMAN, Characterization of complex couple spaces. Ann. Math. 42, 247–250 (1941).

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Last Modified:14 Mar 2016 15:37

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