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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... 
MATHEMATICS | total subspace | MATHEMATICS, APPLIED | Norming subspace | reflexive subspace | M-bibasic system
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 776 - 789
We study the class of Banach spaces X such that the locally convex space (X,μ(X,Y)) is complete for every norming and norm-closed subspace Y... 
Norming subspace | Mackey topology | Mazur property | Completeness | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENTIAL-PROPERTIES
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 5/2015, Volume 31, Issue 5, pp. 767 - 771
Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators... 
46B20 | Mathematics, general | free ultrafilter | 46B10 | Mathematics | Banach space | weak convergence | norming subspace | dual space
Journal Article
ACTA MATHEMATICA SINICA-ENGLISH SERIES, ISSN 1439-8516, 05/2015, Volume 31, Issue 5, pp. 767 - 771
Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators... 
MATHEMATICS | SEQUENTIAL CONVERGENCE | MATHEMATICS, APPLIED | BANACH-SPACES | free ultrafilter | Banach space | weak convergence | norming subspace | dual space
Journal Article
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, 2019, Volume 286, pp. 153 - 174
Conference Proceeding
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 1, pp. 944 - 952
...⁎-dense subspace Y of the dual X⁎ of a Banach space X: (i) The norming character of Y, (ii) the fact that (Y,w⁎) has the Mazur property... 
Norming subspace | Mackey topology | Banach space | Weak compactness | Completeness | Mazur space | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 06/2010, Volume 81, Issue 3, pp. 409 - 413
...* dense subspace Y of the dual X′ of X such that X, endowed with the Mackey topology μ(X,Y ) of the dual pair 〈X,Y 〉, is not complete. 
Krein-Smulyan theorem | Banach spaces | Mackey topologies | norming subspaces | MATHEMATICS
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 479, Issue 1, pp. 608 - 620
A Banach space X has the so-called ball-covering property whenever its unit sphere can be covered by a countable collection of open balls that miss the origin.... 
Renorming | Separability | Norming subspaces | Ball-covering | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES
Journal Article
Note di Matematica, ISSN 1123-2536, 2011, Volume 31, Issue 1, pp. 129 - 138
...^*$ contains a linear subspace $A\subset X^*$ such that the set $A^{(1)}$ of all limits of weak... 
Total subspace | Weak sequential closure | Norming subspace | Quasi-reflexive Banach space | Weak derived set | Weak closure | Mathematics - Functional Analysis
Journal Article
The Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 4/2003, Volume 33, Issue 1, pp. 27 - 67
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 343, Issue 2, pp. 593 - 600
Journal Article
Studia Mathematica, ISSN 0039-3223, 2001, Volume 147, Issue 2, pp. 155 - 168
We study the local dual spaces of a Banach space X, which can be described as the subspaces of X... 
Norming subspace | Local dual space | Local reflexivity | MATHEMATICS | local dual space | PROJECTIONS | local reflexivity | norming subspace
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 08/2000, Volume 175, Issue 1, pp. 168 - 196
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 1/1972, Volume 31, Issue 1, pp. 109 - 111
A Banach space $X$ has a total nonnorming subspace in its dual if and only if $X$ has infinite codimension in its second dual. 
Banach space | Mathematical sequences | Mathematical theorems | Conjugate space | Quasi-reflexive space | Dual space | Norming
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 01/2013, Volume 34, Issue 1, pp. 1 - 15
Let A be a finite subset of ℕ. Consider X: = span{e itk : k ∈ A} and V: = span{e itk : k ∈ B ⊊ A} as subspaces of L p... 
Norming functionals | Minimal projection | Fourier projection | Tensor product | Uniqueness of minimal projection | MATHEMATICS, APPLIED | CONSTANTS | EXTENSIONS | 46B28 | 41A52 | 47A58 | SUBSPACES | TENSOR-PRODUCT-SPACES | Fourier analysis
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2002, Volume 130, Issue 11, pp. 3255 - 3258
...), where X is a Banach space. A local dual space of a Banach space Y is a subspace Z of Y^* so that we have a local representation of Y... 
Abstract spaces | Banach space | Vector valued functions | Banach spaces of vector-valued functions | Norming subspace | Local reflexivity | Local dual space | MATHEMATICS | MATHEMATICS, APPLIED | local dual space | local reflexivity | norming subspace
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 350, Issue 2, pp. 758 - 776
A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space... 
Projection | Projectional skeleton | Projective sequence | Plichko space | Norming set | IDENTITY | MATHEMATICS | MATHEMATICS, APPLIED | VALDIVIA COMPACT SPACES | RESOLUTION | SETS | OPERATORS
Journal Article
Houston Journal of Mathematics, ISSN 0362-1588, 2010, Volume 36, Issue 3, pp. 803 - 821
It is not so difficult to prove that any closed convex solid cone in a Banach space is the union of an unbounded nested sequence of balls in some equivalent... 
Norming cones | Unbounded nested sequences of balls | MATHEMATICS | norming cones
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 8/1985, Volume 94, Issue 4, pp. 665 - 671
We show that the asymptotic-norming and the Radon-Nikodym properties are equivalent, settling a problem of James and Ho [9]. In the process, we give a positive... 
Unit ball | Separable spaces | Mathematical theorems | Banach space | Martingales | Semi-embeddings | Asymptotic-norming and Radon-Nikodym properties
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/1970, Volume 26, Issue 2, pp. 347 - 351
...), where X is a dense subspace of a topological space T. In this paper we obtain several conditions which are equivalent to the following property: every member of P (X... 
Integers | Mathematical theorems | Topological theorems | Algebra | Compactification | Topology | Topological spaces | Seminormalized basis | Complemented subbasis | Equivalent bases | Complementably universal basis | Monotone basis | Subsequence homogeneous norming function | Shrinking basis | Unconditional basis | Universal basis | Boundedly complete basis | Norming function
Journal Article
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