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Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2017, Volume 369, Issue 7, pp. 4671 - 4708
Although our methods are quite general, we are mainly concerned with the choice of X as either a Hilbert space or Ferenczi's uniformly convex Hereditarily... 
MATHEMATICS | ORLICZ SPACES | NONLINEAR CENTRALIZERS | BANACH-SPACES | FAMILIES | 3 SPACE PROBLEM
Journal Article
Journal of the Institute of Mathematics of Jussieu, ISSN 1474-7480, 04/2017, Volume 16, Issue 2, pp. 421 - 445
We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we... 
unitarisable representations | maximal norms | UNIFORMLY BOUNDED REPRESENTATIONS | MATHEMATICS | BANACH-SPACES | NORMS | Graph representations | Hilbert space | Symmetry | Mathematical analysis | Norms | Representations | Banach space | Invariants | Subgroups | Information dissemination | Mathematics - Functional Analysis
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2007, Volume 213, Issue 1, pp. 462 - 488
There exists a real hereditarily indecomposable Banach space X = X ( C ) (respectively X = X ( H ) ) such that the algebra L ( X ) / S ( X ) is isomorphic to C... 
Hereditarily indecomposable | Real Banach space | Unconditional basis | Complex structure | MATHEMATICS | complex structure | real Banach space | unconditional basis | SUBSPACES | hereditarily indecomposable | OPERATORS
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 10/2017, Volume 222, Issue 2, pp. 787 - 814
We investigate complex structures on twisted Hilbert spaces, with special attention paid to the Kalton–Peck Z 2 space and to the hyperplane problem. For any... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | INTERPOLATION | MATHEMATICS | THEOREM | BANACH-SPACES | L-P | SUMS | Hilbert space | Research | Mathematical research | Complex systems
Journal Article
PACIFIC JOURNAL OF MATHEMATICS, ISSN 0030-8730, 07/2019, Volume 301, Issue 1, pp. 31 - 54
Megrelishvili (2001) defines light groups of isomorphisms of a Banach space as the groups on which the weak and strong operator topologies coincide, and proves... 
MATHEMATICS | groups of isomorphisms of Banach spaces | isometry groups | invariant renormings | light groups | renormings of Banach spaces | LUR renormings | Functional Analysis | Mathematics
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 05/2017, Volume 272, Issue 9, pp. 3845 - 3868
A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or “position”) of a Banach space into another and of... 
Automorphic space | Complex structures | Positions of Banach spaces | Borel reducibility | MATHEMATICS | Sorel reducibility | EQUIVALENCE-RELATIONS | UNIQUENESS
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 07/2013, Volume 162, Issue 10, pp. 1771 - 1831
We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group... 
MATHEMATICS | REPRESENTATIONS | PROPERTY | NORM | INDECOMPOSABLE BANACH-SPACES | TRIVIAL ISOMETRIES | OPERATORS | 22F50 | 46B04 | 03E15 | 46B03
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 2006, Volume 156, pp. 125 - 140
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2010, Volume 362, Issue 8, pp. 4385 - 4431
Journal Article
Proceedings of the London Mathematical Society, ISSN 0024-6115, 01/2013, Volume 106, Issue 1, pp. 163 - 202
We define block sequences (xn) in every block subspace of a variant of the space of Gowers and Maurey, so that the map x2n−1↦ x2n extends to an isomorphism.... 
MATHEMATICS | OPERATORS | Isomorphism | Blocking | Sequences | Subspaces | Banach space | Mathematical analysis | Mathematics - Functional Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2014, Volume 410, Issue 2, pp. 670 - 686
We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno and Plichko (2009) [39] and Castillo and Plichko... 
B-convex Banach spaces | Extension of operators | Hereditarily Indecomposable spaces | Hereditarily Indecomposable | MATHEMATICS | 8-convex Banach spaces | MATHEMATICS, APPLIED | THEOREM | MAUREY | SUBSPACES | AUTOMORPHISMS | APPROXIMATION PROPERTY | OPERATORS | GORDON-LEWIS PROPERTY
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2009, Volume 257, Issue 1, pp. 149 - 193
We prove three new dichotomies for Banach spaces à la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal... 
Minimal Banach spaces | Dichotomies | Classification of Banach spaces | MATHEMATICS | BASES | SEQUENCES | UNIVERSAL | DIMENSION | RAMSEY SETS | DICHOTOMY
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2006, Volume 238, Issue 1, pp. 353 - 373
Let X be a Banach space with a Schauder basis ( e n ) n ∈ N . The relation E 0 is Borel reducible to permutative equivalence between normalized block-sequences... 
Dichotomy | Block basis | Homogeneous space | Borel reducibility | Permutative equivalence | MATHEMATICS | THEOREM | dichotomy | FAMILIES | permutative equivalence | block basis | UNCONDITIONAL BASES | SUBSPACES | borel reducibility | homogeneous space | UNIQUENESS
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 12/2006, Volume 156, Issue 1, pp. 125 - 140
If a Banach space is saturated with subspaces with a Schauder basis, which embed into the linear span of any subsequence of their basis, then it contains a... 
Algebra | Analysis | Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2012, Volume 62, Issue 2, pp. 439 - 475
We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them... 
Classification of Banach spaces | Dichotomies | Tight Banach spaces | MATHEMATICS | dichotomies | tight Banach spaces | classification of Banach spaces
Journal Article
Studia Mathematica, ISSN 0039-3223, 2007, Volume 180, Issue 2, pp. 111 - 131
A Banach space X with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if X/Y is hereditarily indecomposable... 
Combinatorial forcing | Gowers' dichotomy theorem | Hereditarily indecomposable | Quotient of subspace | Unconditional basis | MATHEMATICS | quotient of subspace | unconditional basis | gowers' dichotomy theorem | hereditarily indecomposable | combinatorial forcing
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2006, Volume 134, Issue 4, pp. 1039 - 1044
The aim of this note is to prove that if K is any infinite metric compact space, then the Lipschitz free spaces of C(K) and c_0 are isomorphic. This gives an... 
Approximation | Mathematical theorems | Banach space | Homeomorphism | Mathematical lattices | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL UNCONDITIONAL STRUCTURE
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 4/2009, Volume 79, Issue 2, pp. 323 - 345
It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, that is, that any analytic... 
MATHEMATICS | NUMBER | BOREL EQUIVALENCE-RELATIONS | EMBEDDABILITY | FAMILIES | ISOMETRY | FINITELY GENERATED GROUPS
Journal Article
Illinois Journal of Mathematics, ISSN 0019-2082, 09/2005, Volume 49, Issue 3, pp. 839 - 856
For a Banach space X with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subspaces of X as well as for subspaces of X with... 
MATHEMATICS | THEOREM | UNCONDITIONAL BASES
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2005, Volume 195, Issue 1, pp. 259 - 282
We show that any Banach space contains a continuum of non-isomorphic subspaces or a minimal subspace. We define an ergodic Banach space X as a space such that... 
Complexity of isomorphism | Dichotomies for Banach spaces | complexity of isomorphism | MATHEMATICS | dichotomies for Banach spaces
Journal Article
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