Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2018, Volume 464, Issue 2, pp. 1158 - 1166

Continuing the study of preduals of spaces L(H,Y) of bounded, linear maps, we consider the situation that H is a Hilbert space. We establish a natural...

Preduals | Banach algebras | Unique predual | Complemented subspace | MATHEMATICS | MATHEMATICS, APPLIED

Preduals | Banach algebras | Unique predual | Complemented subspace | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2015, Volume 274, pp. 833 - 880

We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis,...

Szlenk index | Embedding into Banach spaces with bases | 46B10 | 46B03 | MATHEMATICS | SUBSPACES | QUOTIENTS | Electrical engineering

Szlenk index | Embedding into Banach spaces with bases | 46B10 | 46B03 | MATHEMATICS | SUBSPACES | QUOTIENTS | Electrical engineering

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 3/2020, Volume 22, Issue 1, pp. 1 - 18

In this paper, we work on Lorentz sequence spaces and explore the fixed point property for $$\ell _{\rho ,\infty }^0$$ ℓρ,∞0 and $$\ell _{\rho ,1}$$ ℓρ,1...

Banach lattice | 46B10 | Mathematics | Nonexpansive mapping | Secondary 46B42 | weak fixed point property | Mathematical Methods in Physics | Primary 46B45 | Lorentz spaces | Analysis | 47H09 | Mathematics, general | fixed point property

Banach lattice | 46B10 | Mathematics | Nonexpansive mapping | Secondary 46B42 | weak fixed point property | Mathematical Methods in Physics | Primary 46B45 | Lorentz spaces | Analysis | 47H09 | Mathematics, general | fixed point property

Journal Article

Formalized Mathematics, ISSN 1426-2630, 10/2017, Volume 25, Issue 3, pp. 179 - 184

In this article, we formalize in the Mizar system [ , ] the F. Riesz theorem. In the first section, we defined Mizar functor , compact topological spaces as...

dual spaces | 46E15 | 46B10 | continuous functions | 03B35 | F. Riesz theorem

dual spaces | 46E15 | 46B10 | continuous functions | 03B35 | F. Riesz theorem

Journal Article

Positivity, ISSN 1385-1292, 7/2018, Volume 22, Issue 3, pp. 711 - 725

Unbounded order convergence has lately been systematically studied as a generalization of almost everywhere convergence to the abstract setting of vector and...

Unbounded order dual | Order continuous predual | Representation of convex functionals | 46B42 | 46B10 | Mathematics | Monotonically complete Banach lattices | 46A20 | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 46E30 | Order continuous dual | Econometrics | MATHEMATICS | Functionals | Lattices (mathematics) | Convergence

Unbounded order dual | Order continuous predual | Representation of convex functionals | 46B42 | 46B10 | Mathematics | Monotonically complete Banach lattices | 46A20 | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 46E30 | Order continuous dual | Econometrics | MATHEMATICS | Functionals | Lattices (mathematics) | Convergence

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 10/2015, Volume 269, Issue 7, pp. 2018 - 2044

This paper will generalize what may be termed the “geometric duality theory” of real pre-ordered Banach spaces which relates geometric properties of a closed...

Duality theory | Cone | Banach space | C-algebra | algebra | FUNDAMENTAL PROPERTIES | MATHEMATICS | ORDERED BANACH-SPACES | Analysis | Algebra | Mathematics - Functional Analysis

Duality theory | Cone | Banach space | C-algebra | algebra | FUNDAMENTAL PROPERTIES | MATHEMATICS | ORDERED BANACH-SPACES | Analysis | Algebra | Mathematics - Functional Analysis

Journal Article

Positivity, ISSN 1385-1292, 11/2019, Volume 23, Issue 5, pp. 1051 - 1064

In the dual $$L_{\varPhi ^*}$$ L Φ ∗ of a $$\varDelta _2$$ Δ 2 -Orlicz space $$L_\varPhi $$ L Φ , that we call a dual Orlicz space, we show that a proper...

Mackey topology | 52A41 | Order closed sets | 46A55 | 46B10 | Mathematics | Komlós’s theorem | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 46E30 | Convex functions | Econometrics | 91G80 | 91B30 | Orlicz spaces | Risk measures | 46B09 | MATHEMATICS | Komlos's theorem

Mackey topology | 52A41 | Order closed sets | 46A55 | 46B10 | Mathematics | Komlós’s theorem | Operator Theory | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | 46E30 | Convex functions | Econometrics | 91G80 | 91B30 | Orlicz spaces | Risk measures | 46B09 | MATHEMATICS | Komlos's theorem

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 5/2013, Volume 10, Issue 2, pp. 927 - 940

We prove that if X is a Banach space and $${f : X \rightarrow \mathbb{R} \cup \{+\infty\}}$$ is a proper function such that f − ℓ attains its minimum for every...

weak compactness | 52A40 | 46A25 | Mathematics, general | 46B10 | reflexive Banach spaces | Mathematics | Convex functions | MATHEMATICS | MATHEMATICS, APPLIED

weak compactness | 52A40 | 46A25 | Mathematics, general | 46B10 | reflexive Banach spaces | Mathematics | Convex functions | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Annales Mathematicae Silesianae, ISSN 0860-2107, 09/2016, Volume 30, Issue 1, pp. 193 - 201

In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we...

smoothness | rotundity | norm derivatives | 46B20 | 46B10 | approximate orthogonality | 46C50 | dual space

smoothness | rotundity | norm derivatives | 46B20 | 46B10 | approximate orthogonality | 46C50 | dual space

Journal Article

10.
Full Text
Simple Proofs of the Uniform Convexity of Lp and the Riesz Representation Theorem for Lp

The American Mathematical Monthly, ISSN 0002-9890, 09/2018, Volume 125, Issue 8, pp. 733 - 738

We give elementary and self-contained proofs of the facts that the L p space with is uniformly convex and its dual space is isometrically isomorphic to .

MSC: Primary 46B10 | Secondary 47J30

MSC: Primary 46B10 | Secondary 47J30

Journal Article

Positivity, ISSN 1385-1292, 3/2018, Volume 22, Issue 1, pp. 59 - 62

We prove that the function and lattice definitions of a narrow operator defined on a Köthe Banach space E on a finite atomless measure space $$(\Omega , \Sigma...

Köthe Banach space | Operator Theory | Fourier Analysis | Potential Theory | Narrow operator | Calculus of Variations and Optimal Control; Optimization | Secondary 46B03 | Vector lattice | Primary 46B20 | 46B10 | Mathematics | Econometrics | MATHEMATICS | Kothe Banach space | Operators (mathematics) | Function space | Banach space | Mathematical analysis | Lattices (mathematics)

Köthe Banach space | Operator Theory | Fourier Analysis | Potential Theory | Narrow operator | Calculus of Variations and Optimal Control; Optimization | Secondary 46B03 | Vector lattice | Primary 46B20 | 46B10 | Mathematics | Econometrics | MATHEMATICS | Kothe Banach space | Operators (mathematics) | Function space | Banach space | Mathematical analysis | Lattices (mathematics)

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 6/2018, Volume 15, Issue 3, pp. 1 - 15

In this note some structural properties of grand variable exponent Lebesgue/Morrey spaces over spaces of homogeneous type are obtained. In particular, it is...

Morrey spaces | 46B26 | grand variable exponent Morrey spaces | predual space | density | Mathematics, general | 46B10 | Mathematics | class of bounded functions | Nakano spaces | Iwaniec–Sbordone space | dual space | MATHEMATICS | MATHEMATICS, APPLIED | Iwaniec-Sbordone space | POTENTIALS | OPERATORS | Control systems | Analysis | Numerical analysis

Morrey spaces | 46B26 | grand variable exponent Morrey spaces | predual space | density | Mathematics, general | 46B10 | Mathematics | class of bounded functions | Nakano spaces | Iwaniec–Sbordone space | dual space | MATHEMATICS | MATHEMATICS, APPLIED | Iwaniec-Sbordone space | POTENTIALS | OPERATORS | Control systems | Analysis | Numerical analysis

Journal Article

Annals of Functional Analysis, ISSN 2008-8752, 2015, Volume 6, Issue 4, pp. 1 - 29

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2016, Volume 43, Issue 1, pp. 135 - 151

We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex...

Komogorov $$\epsilon $$ ϵ -entropy | Packing numbers | 52A10 | Integral constraints | 52A41 | 46B10 | Mathematics | Covering numbers | 41A46 | Numerical Analysis | Analysis | Convex functions | Metric entropy | 54C70

Komogorov $$\epsilon $$ ϵ -entropy | Packing numbers | 52A10 | Integral constraints | 52A41 | 46B10 | Mathematics | Covering numbers | 41A46 | Numerical Analysis | Analysis | Convex functions | Metric entropy | 54C70

Journal Article

Formalized Mathematics, ISSN 1426-2630, 09/2015, Volume 23, Issue 3, pp. 231 - 241

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In...

normed linear spaces | 46E15 | duality and reflexivity | weak topologies | 46B10 | Banach spaces | 03B35 | DUALSP03 | Normed linear spaces

normed linear spaces | 46E15 | duality and reflexivity | weak topologies | 46B10 | Banach spaces | 03B35 | DUALSP03 | Normed linear spaces

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 7/2015, Volume 12, Issue 3, pp. 973 - 986

We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also...

46B28 | proper metric space | Primary 46B10 | Mathematics, general | Mathematics | Secondary 46B04 | bounded approximation property | ultrametric space | duality | Lipschitz-free space | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | LIPSCHITZ-FREE SPACES | APPROXIMATION PROPERTIES

46B28 | proper metric space | Primary 46B10 | Mathematics, general | Mathematics | Secondary 46B04 | bounded approximation property | ultrametric space | duality | Lipschitz-free space | FREE BANACH-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | LIPSCHITZ-FREE SPACES | APPROXIMATION PROPERTIES

Journal Article

Positivity, ISSN 1385-1292, 9/2016, Volume 20, Issue 3, pp. 515 - 539

We show that for a locally $$\sigma $$ σ -finite measure $$\mu $$ μ defined on a $$\delta $$ δ -ring, the associate space theory can be developed as in the...

delta $$ δ -ring | Fatou property | 46B10 | Mathematics | Locally $$\sigma $$ σ -finite measure | Vector measure | Operator Theory | 46G10 | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Banach function space | Order continuous | 46E30 | Econometrics | Associate space

delta $$ δ -ring | Fatou property | 46B10 | Mathematics | Locally $$\sigma $$ σ -finite measure | Vector measure | Operator Theory | 46G10 | Fourier Analysis | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Banach function space | Order continuous | 46E30 | Econometrics | Associate space

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 06/2013, Volume 286, Issue 8‐9, pp. 760 - 771

We extend some fundamental results about the Orlicz space LΦ (such as the Jensen and Hölder inequalities, the LΦ Banach spaces and their duals) to Optimal...

luad spaces MSC Primary: 46E30 | Secondary: 47A63 | optimal Hölder inequality | 46B10 | Optimal Jensen inequality | 47A30 | optimal Orlicz space | Optimal Orlicz space | Luad spaces | Optimal Hölder inequality | MATHEMATICS | optimal Holder inequality

luad spaces MSC Primary: 46E30 | Secondary: 47A63 | optimal Hölder inequality | 46B10 | Optimal Jensen inequality | 47A30 | optimal Orlicz space | Optimal Orlicz space | Luad spaces | Optimal Hölder inequality | MATHEMATICS | optimal Holder inequality

Journal Article

Mathematische Annalen, ISSN 0025-5831, 3/2011, Volume 349, Issue 3, pp. 577 - 588

We prove that a Banach space is reflexive if for every equivalent norm, the set of norm attaining functionals has non-empty norm-interior in the dual space. It...

Mathematics, general | 46B04 | Mathematics | Secondary 46B03 | Primary 46B10 | MATHEMATICS | NORM-ATTAINING FUNCTIONALS | SET

Mathematics, general | 46B04 | Mathematics | Secondary 46B03 | Primary 46B10 | MATHEMATICS | NORM-ATTAINING FUNCTIONALS | SET

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2007, Volume 256, Issue 2, pp. 295 - 300

Isaac Namioka conjectured that every nonreflexive Banach space can be renormed is such a way that, in the new norm, the set of norm attaining functionals has...

Mathematics, general | 46B10 | 46B04 | Mathematics | 46B03 | MATHEMATICS | SET

Mathematics, general | 46B10 | 46B04 | Mathematics | 46B03 | MATHEMATICS | SET

Journal Article

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