Open problems in Banach spaces and measure theory

DOI10.2989/16073606.2017.1315749zbMath1426.28026arXiv1607.07787OpenAlexW2963411362MaRDI QIDQ5236112

Publication date: 15 October 2019

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.07787

zbMATH Keywords

Pettis integral vector measure McShane integral Banach space Riemann integral Borel $\sigma$-algebra Lebesgue-Bochner space measurable selector Baire $\sigma$-algebra

Mathematics Subject Classification ID

Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Vector-valued set functions, measures and integrals (28B05) Compactness in Banach (or normed) spaces (46B50) Nonseparable Banach spaces (46B26)

Cites Work

On coincidence of Pettis and McShane integrability
Weak Compactness in L 1 (μ, X)
Weak Baire measurability of the balls in a Banach space
Compactness in L¹of a vector measure
Remarks on Riemann-integration of vector-valued functions
Biorthogonal systems in Banach spaces
Set-valued analysis
On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
On various modes of scalar convergence in $L_0({\mathfrak X})$
On the weak property of Lebesgue of $L^1(\Omega,\Sigma,\mu)$
Weak continuity of Riemann integrable functions in Lebesgue-Bochner spaces
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Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Riemann integrability versus weak continuity
Convex combinations of weak$^*$-convergent sequences and the Mackey topology
Measurability in $C(2^\kappa)$ and Kunen cardinals
On a certain class of $\mathcal K_{\sigma\delta}$ Banach spaces
Subspaces of $L_p$ that embed into $L_p(\mu)$ with $\mu$ finite
Tukey classification of some ideals on $\omega$ and the lattices of weakly compact sets in Banach spaces
On some problems concerning Borel structures in function spaces
The McShane integral in weakly compactly generated spaces
Boundaries for Banach spaces determine weak compactness
Integration in Hilbert generated Banach spaces
Some approximation properties of Banach spaces and Banach lattices
Lebesgue-Bochner spaces, decomposable sets and strong weakly compact generation
Series in Banach spaces: conditional and unconditional convergence. Transl. from the Russian by Andrei Iacob
On Baire measurability in spaces of continuous functions
Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions
Operators into $L^ 1$ of a vector measure and applications to Banach lattices
On the SWCG property in Lebesgue-Bochner spaces
Weakly extremal properties of Banach spaces
Asymptotic structure of Banach spaces and Riemann integration
On a problem of H.\,P.\ Rosenthal concerning operators on $C$[0,1]
Measurable selectors and set-valued Pettis integral in non-separable Banach spaces
On Banach spaces with the Gelfand-Phillips property
On strongly WCG Banach spaces
Asplund operators and a.e. convergence
Séparabilité vague dans l'espace des mesures sur un compact
Riemann integration in Banach spaces
A decomposition theorem for additive set-functions with applications to Pettis integrals and ergodic means
Espaces de Banachs faiblement K-analytiques
The dual space of ${\mathcal L}^ 1(\mu)$ for a vector measure $\mu$
When $L^ 1$ of a vector measure is an AL-space
On the integration of vector-valued functions
The generalized McShane integral
Kernels of surjections from ${\mathcal L}_1$-spaces with an application to Sidon sets
Banach spaces of vector-valued functions
Hilbert-generated spaces.
When do McShane and Pettis integrals coincide?
On weakly Radon-Nikodým compact spaces
Cofinal types of topological directed orders.
Geometric aspects of convex sets with the Radon-Nikodym property
Some remarks on countably determined measures and uniform distribution of sequences
Three sequential properties of dual Banach spaces in the weak$^*$ topology
On Borel structures in the Banach space $C({\beta}{\omega})$
Multi-applications mesurables à valeurs convexes compactes
Conditional weak compactness in certain inductive tensor products
Some results concerning L$^p(\mu)$-spaces
Banach space theory. The basis for linear and nonlinear analysis
Compactness of the integration operator associated with a vector measure
Factorization of vector measures and their integration operators
Representations of dynamical systems on Banach spaces not containing $l_{1}$
Extension operators on balls and on spaces of finite sets
Summability in L1 of a vector measure
Operator ideal properties of vector measures with finite variation
Weakly compactly generated Banach lattices
A weak$^*$ separable $C(K)^*$ space whose unit ball is not weak$^*$ separable
Weak Compactness and Vector Measures
The Range of a Vector Measure Determines its Total Variation
A new class of weakly countably determined Banach spaces
Weak Cauchy Sequences in L 1 (E)
Pettis integral and measure theory
Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
Reflexivity and Order Properties of Scalar-Type Spectral Operators in Locally Convex Spaces
Limited Operators and Strict Cosingularity
Slicings, Selections and Their Applications
Limited Sets in C(K)‐Spaces and Examples Concerning the Gelfand‐Phillips‐Property
A Characterization of Banach Spaces Containing l ¹
Shorter Notes: L 1 x is Weakly Compactly Generated if x is
An averaging property of the range of a vector measure
Unconditional bases and martingales in L_P(F)
Remarks on the range of a vector measure
Derivability, variation and range of a vector measure
On Pettis integrals with separable range
ON BOREL SETS IN FUNCTION SPACES WITH THE WEAK TOPOLOGY
Banach Space Properties of L 1 of a Vector Measure