3 results
ISOMETRIC REPRESENTATION OF LIPSCHITZ-FREE SPACES OVER CONVEX DOMAINS IN FINITE-DIMENSIONAL SPACES
- Part of
-
- Journal:
- Mathematika / Volume 63 / Issue 2 / 2017
- Published online by Cambridge University Press:
- 04 April 2017, pp. 538-552
- Print publication:
- 2017
-
- Article
- Export citation
-
Let
$E$ be a finite-dimensional normed space and 
$\unicode[STIX]{x1D6FA}$ a non-empty convex open set in 
$E$. We show that the Lipschitz-free space of 
$\unicode[STIX]{x1D6FA}$ is canonically isometric to the quotient of 
$L^{1}(\unicode[STIX]{x1D6FA},E)$ by the subspace consisting of vector fields with zero divergence in the sense of distributions on 
$E$.
EQUILATERAL SETS IN UNIFORMLY SMOOTH BANACH SPACES
- Part of
-
- Journal:
- Mathematika / Volume 60 / Issue 1 / January 2014
- Published online by Cambridge University Press:
- 02 January 2014, pp. 219-231
- Print publication:
- January 2014
-
- Article
- Export citation
-
Let
$X$ be an infinite-dimensional uniformly smooth Banach space. We prove that 
$X$ contains an infinite equilateral set. That is, there exist a constant 
$\lambda \gt 0$ and an infinite sequence 
$\mathop{({x}_{i} )}\nolimits_{i= 1}^{\infty } \subset X$ such that 
$\Vert {x}_{i} - {x}_{j} \Vert = \lambda $ for all 
$i\not = j$.
UNCONDITIONALLY CONVERGENT SERIES OF OPERATORS AND NARROW OPERATORS ON $L_1$
-
- Journal:
- Bulletin of the London Mathematical Society / Volume 37 / Issue 2 / March 2005
- Published online by Cambridge University Press:
- 10 March 2005, pp. 265-274
- Print publication:
- March 2005
-
- Article
- Export citation
