Acta Mathematica Hungarica最新文献_第3页

Inequalities for linear functionals and numerical radii on (mathbf{C}^*)-algebras (mathbf{C}^*) -代数上线性泛函与数值半径的不等式

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-04 DOI: 10.1007/s10474-025-01534-2

P. Bhunia

{"title":"Inequalities for linear functionals and numerical radii on (mathbf{C}^*)-algebras","authors":"P. Bhunia","doi":"10.1007/s10474-025-01534-2","DOIUrl":"10.1007/s10474-025-01534-2","url":null,"abstract":"<div>Let (mathcal{A}) be a unital (mathbf{C}^*)-algebra with unit e.\u0000We develop several inequalities for a positive linear functional f on (mathcal{A}) and obtain several bounds for the numerical radius v(a) of an element (ain mathcal{A}).\u0000Among other inequalities, we show that if (a_k, b_k, x_kin mathcal{A}), (rin mathbb{N}) and (f(e)=1), then\u0000<div><div>$$begin{aligned}\u0000bigg| f bigg( sum_{k=1}^n a_k^*x_kb_kbigg)bigg|^{r} & leq frac{n^{r-1}}{sqrt{2}} bigg| fbigg( sum_{k=1}^n big( (b_k^*|x_k| b_k)^{r}+ i (a_k^*|x_k^*|a_k)^{r} big) bigg) bigg| quad (i=sqrt{-1}), \u0000bigg| fbigg( sum_{k=1}^n a_kbigg)bigg|^{2r} & leq frac{n^{2r-1}}{2} f bigg(sum_{k=1}^n textrm{Re} ( |a_k|^r|a_k^*|^r) + frac{1}{2} sum_{k=1}^n (|a_k|^{2r}+ |a_k^*|^{2r} )bigg).end{aligned}$$</div></div>\u0000We find several equivalent conditions for (v(a)=frac{|a|}{2}) and (v^2(a)={frac{1}{4}|a^*a+aa^*|}).\u0000We prove that (v^2(a)={frac{1}{4}|a^*a+aa^*|}) (resp., (v(a)=frac{|a|}{2})) if and only if \u0000<div><div>$$mathbb{S}_{frac12{ | a^*a+aa^*|}^{1/2}} subseteq V(a) subseteq mathbb{D}_{frac12 {| a^*a+aa^*|}^{1/2}}$$</div></div>\u0000(resp., (mathbb{S}_{frac12 | a|} subseteq V(a) subseteq mathbb{D}_{frac12 | a|})),\u0000where V(a) is the numerical range of a and (mathbb{D}_k) (resp., (mathbb{S}_k)) denotes the circular disk (resp., semi-circular disk) with center at the origin and radius k. We also study inequalities for the ((alpha,beta))-normal elements in (mathcal{A}). </div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"111 - 138"},"PeriodicalIF":0.6,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Largest component in Boolean sublattices 布尔子格中的最大分量

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-04 DOI: 10.1007/s10474-025-01536-0

J. Galliano, R. J. Kang

{"title":"Largest component in Boolean sublattices","authors":"J. Galliano, R. J. Kang","doi":"10.1007/s10474-025-01536-0","DOIUrl":"10.1007/s10474-025-01536-0","url":null,"abstract":"<div>For a subfamily (mathcal{F}subseteq 2^{[n]}) of the Boolean lattice, consider the graph (G_mathcal{F}) on (mathcal{F}) based on the pairwise inclusion relations among its members. Given a positive integer t, how large can (mathcal{F}) be before (G_mathcal{F}) must contain some component of order greater than t?\u0000For t = 1, this question was answered exactly almost a century ago by Sperner: the size of a middle layer of the Boolean lattice. For t = 2n, this question is trivial. We are interested in what happens between these two extremes.\u0000For t = 2g with g = g(n) being any integer function that satisfies (g(n)=o(n/log n)) as (ntoinfty), we give an asymptotically sharp answer to the above question: not much larger than the size of a middle layer.\u0000This constitutes a nontrivial generalisation of Sperner's theorem.\u0000We do so by a reduction to a Turán-type problem for rainbow cycles in properly edge-coloured graphs.\u0000Among other results, we also give a sharp answer to the question, how large can (mathcal{F}) be before (G_mathcal{F})must be connected?</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"183 - 214"},"PeriodicalIF":0.6,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-025-01536-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The categories of corings and coalgebras over a ring are locally countably presentable 环上的心和余代数的范畴是局部可数的

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-04 DOI: 10.1007/s10474-025-01538-y

L. Positselski

引用次数: 0

On the least non-residue in the intersection of a Piatetski–Shapiro sequence and a Beatty sequence 关于Piatetski-Shapiro序列与Beatty序列交点上的最小非残数

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-04 DOI: 10.1007/s10474-025-01537-z

M. Jing

引用次数: 0

Local reflections of choice 选择的本地反思

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-02 DOI: 10.1007/s10474-025-01533-3

C. Ryan-Smith

引用次数: 0

On Wielandt's zipper lemma and (sigma)-subnormal subgroups of finite groups 关于Wielandt的zipper引理和有限群的(sigma) -次正规子群

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-02 DOI: 10.1007/s10474-025-01531-5

F. Aseeri, J. Kaspczyk

引用次数: 0

Substitutions and Cantor real numeration systems 代入与康托实数系统

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-06-02 DOI: 10.1007/s10474-025-01535-1

É. Charlier, C. Cisternino, Z. Masáková, E. Pelantová

{"title":"Substitutions and Cantor real numeration systems","authors":"É. Charlier, C. Cisternino, Z. Masáková, E. Pelantová","doi":"10.1007/s10474-025-01535-1","DOIUrl":"10.1007/s10474-025-01535-1","url":null,"abstract":"<div>We consider Cantor real numeration system as a frame in which every non-negative real number has a positional representation. The system is defined using a bi-infinite sequence (B=(beta_n)_{ninmathbb{Z}}) of real numbers greater than one. We introduce the set of B-integers and code the sequence of gaps between consecutive B-integers by a symbolic sequence in general over the alphabet (mathbb{N}). We show that this sequence is S-adic. We focus on alternate base systems, where the sequence B of bases is periodic, and characterize alternate bases B in which B-integers can be coded by using a symbolic sequence (bf{v}_{it B}) over a finite alphabet. With these so-called Parry alternate bases we associate some morphisms and show that (bf{v}_{it B}) is a fixed point of their composition. We then provide two classes of Parry alternate bases B generating sturmian fixed points. The paper generalizes results of Fabre and Burdík et al. obtained for the Rényi numerations systems, i.e., in the case when the Cantor base B is a constant sequence.</div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"176 1","pages":"15 - 47"},"PeriodicalIF":0.6,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Intersecting families with large shadow degree 具有大阴影度的相交家族

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-22 DOI: 10.1007/s10474-025-01526-2

P. Frankl, J. Wang

引用次数: 0

The isolate bondage number of a graph 图的孤立束缚数

IF 0.6 3区数学

Acta Mathematica Hungarica Pub Date : 2025-05-21 DOI: 10.1007/s10474-025-01523-5

R. Arul Ananthan, S. Balamurugan

引用次数: 0

An alternative equation for generalized polynomials involving measure and category constraints 一个涉及测度约束和范畴约束的广义多项式的替代方程