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Extension of bilinear forms on Banach spaces

Author(s): Jesús M. F. Castillo; Ricardo García; Jesús A. Jaramillo
Journal: Proc. Amer. Math. Soc. 129 (2001), 3647-3656.
MSC (2000): Primary 46B20, 46B28
Posted: June 6, 2001
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Abstract: We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding $j: E \to X$ is said to be (linearly) $N$-exact if $N$-linear forms on $E$ can be (linear and continuously) extended to $X$through $j$. We present some necessary and sufficient conditions for $j$to be $2$-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide.

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Additional Information:

Jesús M. F. Castillo
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, Spain
Email: castillo@unex.es

Ricardo García
Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, Spain
Email: rgarcia@unex.es

Jesús A. Jaramillo
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid, Spain
Email: jaramil@eucmax.sim.ucm.es

DOI: 10.1090/S0002-9939-01-05986-X
PII: S 0002-9939(01)05986-X
Received by editor(s): April 28, 2000
Posted: June 6, 2001
Additional Notes: The research of the first and second authors was supported in part by DGICYT project PB97-0377. The research of the third author was supported by DGICYT project PB96-0607.
Communicated by: Dale Alspach
Copyright of article: Copyright 2001, American Mathematical Society

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