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Monotone gradients on Banach lattices [PDF]

Proceedings of the American Mathematical Society, 1986
It is well known that a differentiable real valued function on the real line is convex iff its derivative is nondecreasing. This characterization of differentiable convex functions does not extend if the domain of the function is a Banach lattice of dim ⩾ 2 \dim \geqslant 2 .
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Sumsets and entropy revisited

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
Abstract The entropic doubling σent[X]$$ {\sigma}_{\mathrm{ent}}\left[X\right] $$ of a random variable X$$ X $$ taking values in an abelian group G$$ G $$ is a variant of the notion of the doubling constant σ[A]$$ \sigma \left[A\right] $$ of a finite subset A$$ A $$ of G$$ G $$, but it enjoys somewhat better properties; for instance, it contracts upon ...
Ben Green, Freddie Manners, Terence Tao
wiley +1 more source

Property (h) of Banach Lattice and Order-to-Norm Continuous Operators

Mathematics, 2023
In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that an order-to-norm continuous operator may not be σ-order continuous.
Fu Zhang, Hanhan Shen, Zili Chen
doaj +1 more source

Asymptotic analysis of a coupled ODE‐PDE system arising from heterogeneous diffusion‐reaction kinetics

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 1, January 2025.
Abstract This contribution is concerned with the well‐posedness and homogenization of an ordinary differential equation (ODE) of Arrhenius‐type coupled with a doubly nonlinear parabolic partial differential equation (PDE) with rapidly oscillating coefficients and taking into account disparate diffusion‐reaction time scales, including regularly as well ...
Michal Beneš, Michael Eden, Adrian Muntean +2 more
wiley +1 more source

On the Quotients of Regular Operators

Universal Journal of Mathematics and Applications, 2019
We give some results about quotients of regular operators on Banach lattices by the linear span of the positive M-weakly and positive L-weakly compact operators.
Erdal Bayram, Cansu Binnaz Binbaşıoğlu +1 more
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ℓp$\ell ^p$ metrics on cell complexes

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Motivated by the observation that groups can be effectively studied using metric spaces modelled on ℓ1$\ell ^1$, ℓ2$\ell ^2$ and ℓ∞$\ell ^\infty$ geometry, we consider cell complexes equipped with an ℓp$\ell ^p$ metric for arbitrary p$p$. Under weak conditions that can be checked locally, we establish non‐positive curvature properties of these
Thomas Haettel, Nima Hoda, Harry Petyt
wiley +1 more source

Common Fixed Point Theorems for Order Contractive Mappings on a σ‐Complete Vector Lattice

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we prove some common fixed point theorems for order contractive mappings on a σ‐complete vector lattice. We apply new results to study the well‐posedness of a common fixed point problem for two contractive mappings. Our proofs are simple and purely order‐theoretic in nature.
Min Wang +4 more
wiley +1 more source

Renorming Dual Banach Lattices [PDF]

Proceedings of the American Mathematical Society, 1982
We show that a Banach lattice is order continuous as well as its dual if and only if it admits an equivalent Fréchet differentiable and locally uniformly convex lattice norm such that its dual norm is also locally uniformly convex.
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Heart failure in Europe: Guideline‐directed medical therapy use and decision making in chronic and acute, pre‐existing and de novo, heart failure with reduced, mildly reduced, and preserved ejection fraction – the ESC EORP Heart Failure III Registry

European Journal of Heart Failure, Volume 26, Issue 12, Page 2487-2501, December 2024.
The ESC Heart Failure III Registry enrolled 10 162 patients between 2018 and 2020, with acute heart failure (HF) and in the outpatient setting, with pre‐existing and de novo HF, in cardiology and non‐cardiology settings, including patients with HF with reduced (HFrEF), mildly reduced (HFmrEF) and preserved ejection fraction (HFpEF).
Lars H. Lund +1226 more
wiley +1 more source

Lattice Ordering on Banach Spaces [PDF]

Proceedings of the American Mathematical Society, 1952
the American Mathematical Society vol. 3 (1952) pp. 821-828. 2. Nils Sjoberg, Sur les minorantes sousharmoniques d'une fonction donnee, Proceedings of the Ninth Scandanavian Mathematical Congress, Helsingfors, 1938, pp. 309-319. 3. Marcel Brelot, Minorantes sous-harmoniques, extremales et capacites, J. Math. Pures Appl. (9) vol. 24 (1945) pp. 1-32.
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