Studia Mathematica, ISSN 0039-3223, 01/2019, Volume 246, Issue 2, pp. 203 - 216

Given a bounded linear operator T from a separable infinite-dimensional Banach space E into a Banach space Y, an operator range R in E and a closed subspace L...

Operator range | Quasicomplemented subspace | Separable Banach space | MATHEMATICS

Operator range | Quasicomplemented subspace | Separable Banach space | MATHEMATICS

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 10/2014, Volume 203, Issue 1, pp. 109 - 140

The Gurariy space G is defined by the property that for every pair of finite dimensional Banach spaces L ⊂ M, every isometry T: L → G admits an extension to an...

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | BANACH-SPACES | Banach spaces | Research | Isomorphisms (Mathematics) | Mathematical research | Mappings (Mathematics)

Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | BANACH-SPACES | Banach spaces | Research | Isomorphisms (Mathematics) | Mathematical research | Mappings (Mathematics)

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2019, Volume 147, Issue 7, pp. 3039 - 3045

We show that if X is a closed subspace of a Banach space E and Z is a closed subspace of E^* such that Z is norming for X and X is total over Z (as well as X...

MATHEMATICS | total subspace | MATHEMATICS, APPLIED | Norming subspace | reflexive subspace | M-bibasic system

MATHEMATICS | total subspace | MATHEMATICS, APPLIED | Norming subspace | reflexive subspace | M-bibasic system

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2015, Volume 143, Issue 11, pp. 4845 - 4849

We show that if X are Banach spaces, where Y is a bounded linear operator such that T^*(Y^*) of X is separable and isomorphic to a polyhedral space. Some...

Polytopes | Boundaries | Renormings | Polyhedral norms | MATHEMATICS | MATHEMATICS, APPLIED | boundaries | polytopes | renormings

Polytopes | Boundaries | Renormings | Polyhedral norms | MATHEMATICS | MATHEMATICS, APPLIED | boundaries | polytopes | renormings

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2014, Volume 420, Issue 1, pp. 94 - 101

We introduce the new concepts of almost overcomplete sequence in a Banach space and almost overtotal sequence in a dual space. We prove that any of such...

Overcomplete sequence | Overtotal sequence | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Functional Analysis

Overcomplete sequence | Overtotal sequence | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Functional Analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 1, pp. 84 - 92

A sequence in a separable Banach space X 〈resp. in the dual space X⁎〉 is said to be overcomplete (OC in short) 〈resp. overtotal (OT in short) on X〉 whenever...

Almost overcomplete sequence | Almost overtotal sequence | MATHEMATICS | MATHEMATICS, APPLIED

Almost overcomplete sequence | Almost overtotal sequence | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Studia Mathematica, ISSN 0039-3223, 2014, Volume 222, Issue 2, pp. 157 - 163

It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space G every finite-dimensional smooth subspace is contained in a bigger...

Spaces of continuous functions | Smooth subspaces | Gurariy space | Lindenstrauss spaces | MATHEMATICS | smooth subspaces | spaces of continuous functions

Spaces of continuous functions | Smooth subspaces | Gurariy space | Lindenstrauss spaces | MATHEMATICS | smooth subspaces | spaces of continuous functions

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 6, pp. 1346 - 1368

We study the relationship between the classical combinatorial inequalities of Simons and the more recent (I)-property of Fonf and Lindenstrauss. We obtain a...

James boundary | Asplund spaces | Banach spaces | MATHEMATICS | SELECTORS | MAPS | SIGMA-FRAGMENTABILITY | LINDELOF PROPERTY | L1 | BANACH-SPACES | CONVEX-SETS

James boundary | Asplund spaces | Banach spaces | MATHEMATICS | SELECTORS | MAPS | SIGMA-FRAGMENTABILITY | LINDELOF PROPERTY | L1 | BANACH-SPACES | CONVEX-SETS

Journal Article

Topology and its Applications, ISSN 0166-8641, 09/2016, Volume 210, pp. 97 - 132

DefinitionLet X be a topological space and G be a subgroup of the group H(X) of all auto-homeomorphisms of X. The pair (X,G) is then called a space-group pair....

Homeomorphism group | Reconstruction | Uniformly continuous | Bilipschitz | Normed spaces | Locally convex spaces | MATHEMATICS | MATHEMATICS, APPLIED

Homeomorphism group | Reconstruction | Uniformly continuous | Bilipschitz | Normed spaces | Locally convex spaces | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

QUARTERLY JOURNAL OF MATHEMATICS, ISSN 0033-5606, 06/2019, Volume 70, Issue 2, pp. 409 - 427

The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder...

MATHEMATICS | SMOOTH | APPROXIMATION | NORMS

MATHEMATICS | SMOOTH | APPROXIMATION | NORMS

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 10/2008, Volume 167, Issue 1, pp. 27 - 48

We show that a one-to-one bounded linear operator T from a separable Banach space E to a Banach space X is a G δ-embedding if and only if every T-null tree in...

Algebra | Mathematical and Computational Physics | Analysis | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics

Algebra | Mathematical and Computational Physics | Analysis | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 01/2014, Volume 266, Issue 1, pp. 247 - 264

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and...

Polytopes | Polyhedral norms and renormings | Boundaries | Countable covers | MATHEMATICS | ORLICZ SEQUENCE-SPACES | APPROXIMATION | BANACH-SPACES | SMOOTH NORMS | RENORMINGS | C(K) | Mathematics - Functional Analysis

Polytopes | Polyhedral norms and renormings | Boundaries | Countable covers | MATHEMATICS | ORLICZ SEQUENCE-SPACES | APPROXIMATION | BANACH-SPACES | SMOOTH NORMS | RENORMINGS | C(K) | Mathematics - Functional Analysis

Journal Article

Canadian Mathematical Bulletin, ISSN 0008-4395, 03/2014, Volume 57, Issue 1, pp. 42 - 50

We prove that, given any covering of any infinite-dimensional Hilbert space H by countably many closed balls, some point exists in H which belongs to...

Hilbert spaces | Slices | Point finite coverings | Polyhedral spaces | MATHEMATICS | slices | polyhedral spaces | point finite coverings

Hilbert spaces | Slices | Point finite coverings | Polyhedral spaces | MATHEMATICS | slices | polyhedral spaces | point finite coverings

Journal Article

Journal of Mathematical Physics, Analysis, Geometry, ISSN 1812-9471, 2013, Volume 9, Issue 1, pp. 108 - 113

We prove two theorems giving sufficient conditions for a Banach space to be isomorphically polyhedral.

Polytopes | Boundaries | Polyhedral norms and renormings | Countable covers | polytopes | polyhedral norms and renormings | CONVEX-BODIES | SECTIONS | boundaries | countable covers | PHYSICS, MATHEMATICAL

Polytopes | Boundaries | Polyhedral norms and renormings | Countable covers | polytopes | polyhedral norms and renormings | CONVEX-BODIES | SECTIONS | boundaries | countable covers | PHYSICS, MATHEMATICAL

Journal Article

Journal of Approximation Theory, ISSN 0021-9045, 2011, Volume 163, Issue 11, pp. 1748 - 1771

In the present paper, we study conditions under which the metric projection of a polyhedral Banach space X onto a closed subspace is Hausdorff lower or upper...

Metric projection | Proximinal subspace | Polyhedral Banach space | MATHEMATICS | CONVEX BODIES | SECTIONS

Metric projection | Proximinal subspace | Polyhedral Banach space | MATHEMATICS | CONVEX BODIES | SECTIONS

Journal Article

Mathematische Annalen, ISSN 0025-5831, 8/2009, Volume 344, Issue 4, pp. 939 - 945

If the unit sphere of a Banach space X can be covered by countably many balls no one of which contains the origin, then, as an easy consequence of the...

46B20 | Mathematics, general | Mathematics | MATHEMATICS | BASIC SEQUENCES | PROPERTY

46B20 | Mathematics, general | Mathematics | MATHEMATICS | BASIC SEQUENCES | PROPERTY

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 350, Issue 2, pp. 640 - 650

A well-known result due to H. Corson states that, for any covering τ by closed bounded convex subsets of any Banach space X containing an infinite-dimensional...

Covering | Finitely locally finite covering | Locally finite covering | MATHEMATICS | MATHEMATICS, APPLIED | BASIC SEQUENCES

Covering | Finitely locally finite covering | Locally finite covering | MATHEMATICS | MATHEMATICS, APPLIED | BASIC SEQUENCES

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 255, Issue 2, pp. 449 - 470

We prove the existence of equivalent polyhedral norms on a number of classes of non-separable spaces, the majority of which being of the form C ( K ) . In...

Polyhedral norm | Tree | Orlicz space | Scattered compact | MATHEMATICS | polyhedral norm | CONVEX-BODIES | APPROXIMATION | scattered compact | tree

Polyhedral norm | Tree | Orlicz space | Scattered compact | MATHEMATICS | polyhedral norm | CONVEX-BODIES | APPROXIMATION | scattered compact | tree

Journal Article

Topology and its Applications, ISSN 0166-8641, 2008, Volume 155, Issue 14, pp. 1627 - 1633

The following properties of the Holmes space H are established: (i) H has the Metric Approximation Property (MAP). (ii) The w ∗ -closure of the set of extreme...

Metric approximation property | Non-complemented subspaces | Holmes space | Urysohn space | Extreme points | MATHEMATICS | MATHEMATICS, APPLIED | L1 SPACES | DUALS | metric approximation property | non-complemented subspaces | BANACH-SPACES | extreme points

Metric approximation property | Non-complemented subspaces | Holmes space | Urysohn space | Extreme points | MATHEMATICS | MATHEMATICS, APPLIED | L1 SPACES | DUALS | metric approximation property | non-complemented subspaces | BANACH-SPACES | extreme points

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 12/2010, Volume 179, Issue 1, pp. 479 - 491

We construct on any quasi-reflexive of order 1 separable real Banach space an equivalent norm, such that all contractions on the space and all contractions on...

Algebra | Theoretical, Mathematical and Computational Physics | Analysis | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | EXTREME POINTS | Banach spaces | Research

Algebra | Theoretical, Mathematical and Computational Physics | Analysis | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | EXTREME POINTS | Banach spaces | Research

Journal Article

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