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

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

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

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

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

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

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

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

A group G is representable in a Banach space X if G is isomorphic to the group of isometries on X in some equivalent norm. We prove that a countable group G is...

Unit ball | Line segments | Topological theorems | Separable spaces | Group isomorphism | Mathematical vectors | Strong operator topologies | Banach space | Lurs | Group of isometries on banach spaces | Complex structures up to isometry | Group representable in a banach space | MATHEMATICS | complex structures up to isometry | group representable in a Banach space | TRIVIAL ISOMETRIES | COMPLEX STRUCTURE | OPERATORS | Group of isometrics on Banach spaces | UNIQUENESS

Unit ball | Line segments | Topological theorems | Separable spaces | Group isomorphism | Mathematical vectors | Strong operator topologies | Banach space | Lurs | Group of isometries on banach spaces | Complex structures up to isometry | Group representable in a banach space | MATHEMATICS | complex structures up to isometry | group representable in a Banach space | TRIVIAL ISOMETRIES | COMPLEX STRUCTURE | OPERATORS | Group of isometrics on Banach spaces | UNIQUENESS

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

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

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

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

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

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

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

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

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

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

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

Complexity of isomorphism | Dichotomies for Banach spaces | complexity of isomorphism | MATHEMATICS | dichotomies for Banach spaces

Journal Article

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