On the ℓ1 non-embedding in the James Tree Space

2020 ◽  
Vol 38 (1) ◽  
pp. 112-130
Author(s):  
Ioakeim Ampatzoglou
Keyword(s):  
Tree Space

Projections on Tree-Like banach Spaces

1985 ◽  
Vol 37 (5) ◽  
pp. 908-920
Author(s):  
A. D. Andrew
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Unconditional Basis ◽  
Reflexive Banach Space ◽  
Separable Space ◽  
Bounded Linear ◽  
Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

scholarly journals Computing Geodesic Distances in Tree Space

2011 ◽  
Vol 25 (4) ◽  
pp. 1506-1529 ◽  
Author(s):  
Megan Owen
Keyword(s):  
Tree Space ◽  
Geodesic Distances

scholarly journals The dual of the James tree space is asymptotically uniformly convex

2001 ◽  
Vol 147 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Maria Girardi
Keyword(s):  
Uniformly Convex ◽  
Tree Space

scholarly journals Tree-Space Statistics and Approximations for Large-Scale Analysis of Anatomical Trees

2013 ◽  
pp. 74-85 ◽  
Author(s):  
Aasa Feragen ◽  
Megan Owen ◽  
Jens Petersen ◽  
Mathilde M. W. Wille ◽  
Laura H. Thomsen ◽  
...  
Keyword(s):  
Large Scale ◽  
Scale Analysis ◽  
Large Scale Analysis ◽  
Tree Space

Some Results about Stopping Timesof the Marked Tree Space

1997 ◽  
Vol 41 (3) ◽  
pp. 425-435
Author(s):  
C. Ceci ◽  
A. Gerardi ◽  
L. Mazliak
Keyword(s):  
Tree Space

Sampling phylogenetic tree space with the generalized Gibbs sampler

Cladistics ◽  
2014 ◽  
Vol 31 (4) ◽  
pp. 438-440
Author(s):  
Jonathan M. Keith
Keyword(s):  
Phylogenetic Tree ◽  
Gibbs Sampler ◽  
Tree Space

scholarly journals Empirical Analysis of Phylogenetic Quasi-Terraces

2019 ◽  
Author(s):  
Paula Breitling ◽  
Alexandros Stamatakis ◽  
Olga Chernomor ◽  
Ben Bettisworth ◽  
Lukasz Reszczynski
Keyword(s):  
Phylogenetic Tree ◽  
Search Algorithms ◽  
Data Sets ◽  
Tree Search ◽  
Significance Tests ◽  
Analogous Structure ◽  
Phylogenetic Studies ◽  
Log Likelihood ◽  
Tree Space ◽  
Nearest Neighborhood

AbstractTerraces in phylogenetic tree space are, among other things, important for the design of tree space search strategies. While the phenomenon of phylogenetic terraces is already known for unlinked partition models on partitioned phylogenomic data sets, it has not yet been studied if an analogous structure is present under linked and scaled partition models. To this end, we analyze aspects such as the log-likelihood distributions, likelihood-based significance tests, and nearest neighborhood interchanges on the trees residing on a terrace and compare their distributions among unlinked, linked, and scaled partition models. Our study shows that there exists a terrace-like structure under linked and scaled partition models as well. We denote this phenomenon as quasi-terrace. Therefore quasi-terraces should be taken into account in the design of tree search algorithms as well as when reporting results on ‘the’ final tree topology in empirical phylogenetic studies.

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