On $$A_1^2$$ A 1 2 restrictions of Weyl arrangements

Journal of Algebraic Combinatorics - Let $$\mathcal {A}$$ be a Weyl arrangement in an $$\ell $$ -dimensional Euclidean space. The freeness of restrictions of $$\mathcal {A}$$ was first settled by a...     

Pro- $$\mathcal {C}$$ C congruence properties for groups of rooted tree automorphisms

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro- $$\mathcal {C}$$ completions of the group, where $$\mathcal {C}$$ is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the $$\mathcal {C}$$ -congruence subgroup property ( $$\mathcal {C}$$ -CSP) if its pro- $$\mathcal {C}$$ completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the $$\mathcal {C}$$ -CSP. In the case where $$\mathcal {C}$$ is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.     

Infinite number of eigenvalues of $$2{\times}2$$ operator matrices: Asymptotic discrete spectrum

Theoretical and Mathematical Physics - We study an unbounded $$2{\times}2$$ operator matrix $$ \mathcal{A} $$ in the direct product of two Hilbert spaces. We obtain asymptotic formulas for the...     

Compact Operators and Uniform Structures in Hilbert $$C^*$$ -Modules

Functional Analysis and Its Applications - Quite recently a criterion for the $$\mathcal{A}$$ -compactness of an ajointable operator $$F\colon {\mathcal M} \to\mathcal{N}$$ between Hilbert $$C^*$$...     

Nonlinear Triple Product $$A^{*}B + B^{*}A$$ for Derivations on $$\ast$$ -Algebras

Mathematical Notes - Let $$\mathcal{A}$$ be a prime $$\ast$$ -algebra. In this paper, assuming that $$\Phi:\mathcal{A}\to\mathcal{A}$$ satisfies $$\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B...     

The completeness characterization of $$C(\mathcal {L})$$ C ( L ) , $$\mathcal {L}$$ L a locale

Positivity - The result of the title is: an archimedean $$\ell $$ -group with weak unit A is (isomorphic to) $$C(\mathcal {L})$$ for some (identifiable) locale $$\mathcal {L}$$ (or, $$\mathbb...     

A class of multipliers for $$\mathcal{W}^ \bot $$

Let denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let be the class of multipliers for , i.e. ergodic transformations whose all ergodic joinings with any element of are also in . Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of . Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations. Dedicated to Hillel Furstenberg on the occasion of his retirement The first-named author was supported in part by CRDF, grant UM1-2546-KH-03. The second-named author was supported in part by KBN grant 1P03A 03826.     

Codes defined by forms of degree 2 on non-degenerate Hermitian varieties in $${\mathbb{P}^{4}(\mathbb{F}_q)}$$

We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular Hermitian variety .      

Dy namic of Abelia n Subgroups of GL( n, $$\mathbb{C}$$): A Structure Theorem

In this paper, we characterize the dynamic of every Abelian subgroups of , or . We show that there exists a -invariant, dense open set U in saturated by minimal orbits with a union of at most n -invariant vector subspaces of of dimension n−1 or n−2 over . As a consequence, has height at most n and in particular it admits a minimal set in . This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15     

Dark $$f(\mathcal{R},\varphi,\chi)$$ universe with Noether symmetry

Theoretical and Mathematical Physics - Using the Noether symmetry approach, we investigate $$f( \mathcal{R} , \varphi ,\chi)$$ theories of gravity, where $$ \mathcal{R} $$ is the scalar curvature,...     

A note on strong skew Jordan product preserving maps on von Neumann algebras

Periodica Mathematica Hungarica - Let $$\mathcal {A}$$ be a von Neumann algebra acting on the complex Hilbert space $$\mathcal {H}$$ and $$\Phi {:}\,\mathcal {A} \longrightarrow \mathcal {A}$$ be a...     

A Sharp Weak-Type $$(\infty ,\infty )$$ Inequality for the Hilbert Transform

The paper is devoted to sharp weak type \((\infty ,\infty )\) estimates for \({\mathcal {H}}^{\mathbb {T}}\) and \({\mathcal {H}}^{\mathbb {R}}\), the Hilbert transforms on the circle and real line, respectively. Specifically, it is proved that

$$\begin{aligned} \left\| {\mathcal {H}}^{\mathbb {T}}f\right\| _{W({\mathbb {T}})}\le \Vert f\Vert _{L^\infty ({\mathbb {T}})} \end{aligned}$$

and

$$\begin{aligned} \left\| {\mathcal {H}}^{\mathbb {R}}f\right\| _{W({\mathbb {R}})}\le \Vert f\Vert _{L^\infty ({\mathbb {R}})}, \end{aligned}$$

where \(W({\mathbb {T}})\) and \(W({\mathbb {R}})\) stand for the weak-\(L^\infty \) spaces introduced by Bennett, DeVore and Sharpley. In both estimates, the constant \(1\) on the right is shown to be the best possible.

     

A uniform version of a theorem by Dvir and Moran

Acta Mathematica Hungarica - Let $$0\leq d\leq n$$ be integers and $$\mathcal{F}$$ a family with $${\rm VCdim} ( \mathcal{F} \Delta \mathcal{F} )\leq d$$ . Analogously to the celebrated...     

Spectral Shorted Operators

If $$\mathcal{H}$$ is a Hilbert space, $$\mathcal{S}$$ is a closed subspace of $$\mathcal{H},$$ and A is a positive bounded linear operator on $$\mathcal{H},$$ the spectral shorted operator $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence $$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes $$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to $$\mathcal{S}.$$ We characterize the left spectral resolution of $$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ and show several properties of this operator, particularly in the case that dim $${\mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional case and for non invertible operators.     

Matroid bases with cardinality constraints on the intersection

Mathematical Programming - Given two matroids $$\mathcal {M}_{1} = (E, \mathcal {B}_{1})$$ and $$\mathcal {M}_{2} = (E, \mathcal {B}_{2})$$ on a common ground set E with base sets $$\mathcal...     

Maps preserving a certain product of operators

Let $$\mathcal {A}$$ be a standard operator algebra on a Banach space $$\mathcal {X}$$ with $$ \dim \mathcal {X}\ge 3$$. In this paper, we determine the form of the bijective maps $$\phi :\mathcal {A}\longrightarrow \mathcal {A}$$ satisfying $$\begin{aligned} \phi \left( \frac{1}{2}(AB^2+B^2A)\right) = \frac{1}{2}[\phi (A)\phi (B)^{2}+\phi (B)^{2}\phi (A)], \end{aligned}$$for every $$A,B \in \mathcal {A}$$.     

On the Hilbert scheme of linearly normal curves in $$\mathbb {P}^4$$ P 4 of degree $$d = g+1$$ d = g + 1 and genus g

Archiv der Mathematik - We denote by $$\mathcal {H}_{d,g,r}$$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and...     

Anti-derivable linear maps at zero on standard operator algebras

Acta Mathematica Hungarica - Let $$\mathcal{X}$$ be a complex Banach space with $$\dim \mathcal{X}\geq 2$$ , and $$\mathcal{A} \subseteq \mathcal{B}(\mathcal{X})$$ be a standard operator algebra....     

A category analogue of the density topology non-homeomorphic with the $$\mathcal {I}$$ I -density topology

Positivity - The paper deals with the category analogue of a density point and a density topology (with respect to a Lebesgue measure) on the real line which is different from the $$\mathcal {I}$$...     

Counter-examples to the Dunford–Schwartz pointwise ergodic theorem on $$\varvec{L^1+L^\infty }$$ L 1 + L ∞

Extending a result by Chilin and Litvinov, we show by construction that given any $$\sigma $$ -finite infinite measure space $$(\Omega ,\mathcal {A}, \mu )$$ and a function $$f\in L^1(\Omega )+L^\infty (\Omega )$$ with $$\mu (\{|f|>\varepsilon \})=\infty $$ for some $$\varepsilon >0$$ , there exists a Dunford–Schwartz operator T over $$(\Omega ,\mathcal {A}, \mu )$$ such that $$\frac{1}{N}\sum _{n=1}^N (T^nf)(x)$$ fails to converge for almost every $$x\in \Omega $$ . In addition, for each operator we construct, the set of functions for which pointwise convergence fails almost everywhere is residual in $$L^1(\Omega )+L^\infty (\Omega )$$ .