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James Tree Space

A James tree space is a completion of finitely supported real scalar arrays on a rooted tree with the segment norm

rho(a)=sup[sum_(i=1)^m(sum_(v in S_i)a_v)^2]^(1/2),

where the supremum runs over finite families of pairwise disjoint tree segments. A segment is a finite consecutive part of a root path. The underlying tree is specified in each construction. The classical construction uses the binary tree. The same segment-norm construction also applies to trees with countable branching.

See also

Asymptotic Midpoint Uniform Convexity, Asymptotic Uniform Convexity, Bi-Lipschitz Map, Dual Normed Space, Reflexive Space, Tree

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References

Avilés, A. "Renormings of the Dual of James Tree Spaces." Bull. London Math. Soc. 39, 221-231, 2007. https://doi.org/10.1112/blms/bdl040.

Cite this as:

Weisstein, Eric W. "James Tree Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JamesTreeSpace.html

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