## Banach Journal of Mathematical Analysis

### On certain uniformly open multilinear mappings

#### Abstract

We obtain two results stating the uniform openness of bilinear operators and multilinear functionals. The first result deals with Banach spaces $L^{p}:=L_{\mathbb{K}}^{p}$ (over $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$) and pointwise multiplication from $L^{p}\times L^{q}$ to $L^{r}$ (where $1/p+1/q=1/r$). The second result is concerned with the nontrivial $n$-linear functionals from the product $X_{1}\times\cdots\times X_{n}$ of normed spaces (over $\mathbb{K}\in\{\mathbb{R},\mathbb{C}\}$) to the field $\mathbb{K}$.

#### Article information

Source
Banach J. Math. Anal., Volume 10, Number 3 (2016), 482-494.

Dates
Accepted: 2 October 2015
First available in Project Euclid: 13 May 2016

https://projecteuclid.org/euclid.bjma/1463153912

Digital Object Identifier
doi:10.1215/17358787-3599741

Mathematical Reviews number (MathSciNet)
MR3504181

Zentralblatt MATH identifier
1356.46014

#### Citation

Balcerzak, Marek; Behrends, Ehrhard; Strobin, Filip. On certain uniformly open multilinear mappings. Banach J. Math. Anal. 10 (2016), no. 3, 482--494. doi:10.1215/17358787-3599741. https://projecteuclid.org/euclid.bjma/1463153912

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