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In this paper we study weakly almost periodic and uniformly continuous functionals on the Orlicz Fig\`a-Talamanca Herz algebras associated to a locally compact group. We show that a unique invariant mean exists on the space of weakly almost…

Functional Analysis · Mathematics 2019-09-16 Rattan Lal , N. Shravan Kumar

Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…

Functional Analysis · Mathematics 2015-11-05 Moritz Gerlach , Markus Kunze

We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…

Commutative Algebra · Mathematics 2016-09-07 Silvano Baggio

We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every chain complete, rooted tree into a Fr\'echet--Urysohn,…

General Topology · Mathematics 2022-03-16 Tommaso Russo , Jacopo Somaglia

We discuss the rainbow Ramsey theorems at limit cardinals and successors of singular cardinals, addressing some questions in \cite{MR2354904} and \cite{MR2902230}. In particular, we show for inaccessible $\kappa$,…

Logic · Mathematics 2019-12-03 Jing Zhang

Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue…

Logic · Mathematics 2014-04-08 Paolo Lipparini

Non-compact proofs are a class of reasoning that is used in mathematics but overlooked in the analysis of (un)provability of consistency. We focus on proofs of arithmetical statements (*) "for any natural number n, F(n)." A proof of (*) is…

Logic · Mathematics 2025-12-16 Sergei Artemov

A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model. Assume that kappa is a countably closed…

Logic · Mathematics 2016-09-07 William J. Mitchell , Ernest Schimmerling , John R. Steel

We prove a certain 'fat hyperplane section' Weak Lefschetz-type theorem for etale cohomology of non-projective varieties, similar to a result of Goresky and MacPherson (over complex numbers). This statement easily yields certain (vast)…

Algebraic Geometry · Mathematics 2015-02-03 Mikhail V. Bondarko

We investigate the provability of classical combinatorial theorems in ZF. Using combinatorial arguments, we establish the following results for each infinite cardinal ${\kappa}\in On$, (1) ${\kappa}^+\to ({\kappa},{\omega}+1)$, (2) any…

Logic · Mathematics 2023-06-13 Tamás Csernák , Lajos Soukup

It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…

Functional Analysis · Mathematics 2019-02-26 Isabelle Chalendar , Jonathan R. Partington

We investigate the consistency strength of the statement: $\kappa$ is weakly compact and there is no tree on $\kappa$ with exactly $\kappa^{+}$ many branches. We show that this statement fails strongly (in the sense that there is a sealed…

Logic · Mathematics 2021-09-22 Yair Hayut , Sandra Müller

We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups. For…

Dynamical Systems · Mathematics 2024-01-17 Andy Zucker

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

Logic · Mathematics 2019-07-12 Marta Bílková , Almudena Colacito

We show that a composition operator induced by an analytic self-map of the unit disc in the complex plane is weakly compact on the space BMOA precisely when the operator is compact on BMOA. As a crucial step we simplify the compactness…

Functional Analysis · Mathematics 2010-01-22 Jussi Laitila , Pekka J. Nieminen , Eero Saksman , Hans-Olav Tylli

In this paper, we study a class of Banach spaces, called \phi-spaces. In a natural way, we associate a measure of weak compactness in such spaces and prove an analogue of Sadovskii fixed point theorem for weakly sequentially continuous…

Functional Analysis · Mathematics 2007-05-23 Cleon S. Barroso , Donal O'Regan

The {\em Singular Cardinal Hypothesis} (SCH) is one of the most classical combinatorial principles in set theory. It says that if $\kappa$ is singular strong limit, then $2^{\kappa}=\kappa^+$. We prove that given a singular cardinal…

Logic · Mathematics 2022-02-23 Sittinon Jirattikansakul

In this paper we prove that if $\Lambda\in M_p(\mathbb R^N)$ and has compact support then $\Lambda$ is a weak summability kernel for $1<p<\infty$, where $M_p(\mathbb R^N)$ is the space of multipliers of $L^p(\mathbb R^N)$.

Functional Analysis · Mathematics 2007-05-23 P. Mohanty , S. Madan

Monotone triangles are a rich extension of permutations that biject with alternating sign matrices. The notions of weak order and descent sets for permutations are generalized here to monotone triangles, and shown to enjoy many analogous…

Combinatorics · Mathematics 2019-05-24 Zachary Hamaker , Victor Reiner

Weak gravitational lensing of background galaxies provides a direct probe of the projected matter distribution in and around galaxy clusters. Here we present a self-contained pedagogical review of cluster--galaxy weak lensing, covering a…

Cosmology and Nongalactic Astrophysics · Physics 2020-12-15 Keiichi Umetsu