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January 2016 Multipliers and Hadamard products in the vector-valued setting
Óscar Blasco, Carme Zaragoza-Berzosa
Banach J. Math. Anal. 10(1): 71-95 (January 2016). DOI: 10.1215/17358787-3319378

Abstract

Let Ei be Banach spaces, and let XEi be Banach spaces continuously contained in the spaces of Ei-valued sequences (xˆ(j))jEiN, for i=1,2,3. Given a bounded bilinear map B:E1×E2E3, we define (XE2,XE3)B, the space of B-multipliers between XE2 and XE3, to be the set of sequences (λj)jE1N such that (B(λj,xˆ(j)))jXE3 for all (xˆ(j))jXE2, and we define the Hadamard projective tensor product XE1BXE2 as consisting of those elements in E3N that can be represented as njB(xˆn(j),yˆn(j)), where (xn)nXE1, (yn)nXE2, and nxnXE1ynXE2<.

We will analyze some properties of these two spaces, relate them, and compute the Hadamard tensor products and the spaces of vector-valued multipliers in several cases, getting applications in the particular case where E=L(E1,E2) and B(T,x)=T(x).

Citation

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Óscar Blasco. Carme Zaragoza-Berzosa. "Multipliers and Hadamard products in the vector-valued setting." Banach J. Math. Anal. 10 (1) 71 - 95, January 2016. https://doi.org/10.1215/17358787-3319378

Information

Received: 11 December 2014; Accepted: 14 April 2015; Published: January 2016
First available in Project Euclid: 11 November 2015

zbMATH: 1352.46020
MathSciNet: MR3453524
Digital Object Identifier: 10.1215/17358787-3319378

Subjects:
Primary: 46B28
Secondary: 46E40

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 1 • January 2016
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