Dissertationes Mathematicae最新文献_第3页

On the $K$-theory of $C^*$-algebras associated to substitution tilings C^*$-代数的K$-理论与替换平铺

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/dm800-4-2020

D. Gonçalves, Maria Ramirez-Solano

引用次数: 2

Generalized $T^p_u$ spaces: On the trail of Calderón and Zygmund 广义的$T^p_u$空间:关于Calderón和Zygmund的线索

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/dm798-4-2020

L. Loosveldt, S. Nicolay

引用次数: 5

On differential invariants of parabolic surfaces 关于抛物曲面的微分不变量

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-08-21 DOI: 10.4064/DM816-8-2020

Zhangchi Chen, J. Merker

引用次数: 14

On the numerical index with respect to an operator 关于一个运算符的数值索引

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-05-29 DOI: 10.4064/dm805-9-2019

V. Kadets, Miguel Martín, Javier Merí, Antonio Pérez, Alicia Quero

{"title":"On the numerical index with respect to an operator","authors":"V. Kadets, Miguel Martín, Javier Merí, Antonio Pérez, Alicia Quero","doi":"10.4064/dm805-9-2019","DOIUrl":"https://doi.org/10.4064/dm805-9-2019","url":null,"abstract":"Given Banach spaces $X$ and $Y$, and a norm-one operator $Gin mathcal{L}(X,Y)$, the numerical index with respect to $G$, $n_G(X,Y)$, is the greatest constant $kgeq 0$ such that $$max_{|w|=1}|G+wT|geq 1 + k |T|$$ for all $Tin mathcal{L}(X,Y)$. We present some results on the set $mathcal{N}(mathcal{L}(X,Y))$ of the values of the numerical indices with respect to all norm-one operators on $mathcal{L}(X,Y)$. We show that $mathcal{N}(mathcal{L}(X,Y))={0}$ when $X$ or $Y$ is a real Hilbert space of dimension greater than one and also when $X$ or $Y$ is the space of bounded or compact operators on an infinite-dimensional real Hilbert space. For complex Hilbert spaces $H_1$, $H_2$ of dimension greater than one, we show that $mathcal{N}(mathcal{L}(H_1,H_2))subseteq {0,1/2}$ and the value $1/2$ is taken if and only if $H_1$ and $H_2$ are isometrically isomorphic. Besides, $mathcal{N}(mathcal{L}(X,H))subseteq [0,1/2]$ and $mathcal{N}(mathcal{L}(H,Y))subseteq [0,1/2]$ when $H$ is a complex infinite-dimensional Hilbert space and $X$ and $Y$ are arbitrary complex Banach spaces. We also show that $mathcal{N}(mathcal{L}(L_1(mu_1),L_1(mu_2)))subseteq {0,1}$ and $mathcal{N}(mathcal{L}(L_infty(mu_1),L_infty(mu_2)))subseteq {0,1}$ for arbitrary $sigma$-finite measures $mu_1$ and $mu_2$, in both the real and the complex cases. Also, we show that the Lipschitz numerical range of Lipschitz maps can be viewed as the numerical range of convenient bounded linear operators with respect to a bounded linear operator. Further, we provide some results which show the behaviour of the value of the numerical index when we apply some Banach space operations, as constructing diagonal operators between $c_0$-, $ell_1$-, or $ell_infty$-sums of Banach spaces, composition operators on some vector-valued function spaces, and taking the adjoint to an operator.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2019-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41688177","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: 3

Characterizations of derivations 衍生物的特征

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-04-01 DOI: 10.4064/DM775-9-2018

E. Gselmann

{"title":"Characterizations of derivations","authors":"E. Gselmann","doi":"10.4064/DM775-9-2018","DOIUrl":"https://doi.org/10.4064/DM775-9-2018","url":null,"abstract":"The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 we collect all the definitions and results regarding derivations that are essential while studying this area. \u0000In Chapter 3 we intend to show that derivations can be characterized by one single functional equation. More exactly, we study here the following problem. Let $Q$ be a commutative ring and let $P$ be a subring of $Q$. Let $lambda, muin Qsetminusleft{0right}$ be arbitrary, $fcolon Prightarrow Q$ be a function and consider the equation [ lambdaleft[f(x+y)-f(x)-f(y)right]+ muleft[f(xy)-xf(y)-yf(x)right]=0 quad left(x, yin Pright). ] In this chapter it will be proved that under some assumptions on the rings $P$ and $Q$, derivations can be characterized via the above equation. \u0000Chapter 4 is devoted to the additive solvability of a system of functional equations. Moreover, the linear dependence and independence of the additive solutions $d_{0},d_{1},dots,d_{n} colonmathbb{R}tomathbb{R}$ of the above system of equations is characterized. \u0000Finally, the closing chapter deals with the following problem. Assume that $xicolon mathbb{R}to mathbb{R}$ is a given differentiable function and for the additive function $fcolon mathbb{R}to mathbb{R}$, the mapping [ \u0000varphi(x)=fleft(xi(x)right)-xi'(x)f(x) ] fulfills some regularity condition on its domain. Is it true that in such a case $f$ is a sum of a derivation and a linear function?","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43525701","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: 1

Greedy approximation for biorthogonal systems in quasi-Banach spaces 拟banach空间中双正交系统的贪心逼近

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-03-27 DOI: 10.4064/DM817-11-2020

F. Albiac, J. L. Ansorena, P. M. Berná, P. Wojtaszczyk

引用次数: 52

Existence and regularity of invariant graphs for cocycles in bundles: partial hyperbolicity case 束中环不变图的存在性与正则性:部分双曲情况

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-03-18 DOI: 10.4064/DM799-4-2020

Deliang Chen

引用次数: 1

The forgotten mathematical legacy of Peano 皮诺被遗忘的数学遗产