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2013 OPENNESS OF MULTIPLICATION IN SOME FUNCTION SPACES
Marek Balcerzak, Adam Majchrzycki, Artur Wachowicz
Taiwanese J. Math. 17(3): 1115-1126 (2013). DOI: 10.11650/tjm.17.2013.2521

Abstract

We show that, for several function Banach spaces, multiplication considered as a bilinear continuous srjection, is an open mapping. In particular, we prove that multiplication from $L_p \times L_q$ to $L_1$ (for $p,q \in [1,\infty]$, $1/p + 1/q = 1$) is open.

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Marek Balcerzak. Adam Majchrzycki. Artur Wachowicz. "OPENNESS OF MULTIPLICATION IN SOME FUNCTION SPACES." Taiwanese J. Math. 17 (3) 1115 - 1126, 2013. https://doi.org/10.11650/tjm.17.2013.2521

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1292.46009
MathSciNet: MR3072279
Digital Object Identifier: 10.11650/tjm.17.2013.2521

Subjects:
Primary: 46B25 , 47A06 , 54C10

Keywords: $l_p$ spaces , classical Banach spaces , multiplication , open mapping

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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Vol.17 • No. 3 • 2013
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