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Outgoing monotone geodesics of standard subspaces 标准子空间的外向单调大地线
arXiv - MATH - Functional Analysis Pub Date : 2024-09-12 DOI: arxiv-2409.08184
Jonas Schober
{"title":"Outgoing monotone geodesics of standard subspaces","authors":"Jonas Schober","doi":"arxiv-2409.08184","DOIUrl":"https://doi.org/arxiv-2409.08184","url":null,"abstract":"We prove a real version of the Lax-Phillips Theorem and classify outgoing\u0000reflection positive orthogonal one-parameter groups. Using these results, we\u0000provide a normal form for outgoing monotone geodesics in the set Stand(H) of\u0000standard subspaces on some complex Hilbert space H. As the modular operators of\u0000a standard subspace are closely related to positive Hankel operators, our\u0000results are obtained by constructing some explicit symbols for positive Hankel\u0000operators. We also describe which of the monotone geodesics in Stand(H) arise\u0000from the unitary one-parameter groups described in Borchers' Theorem and\u0000provide explicit examples of monotone geodesics that are not of this type.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The $H^infty$-functional calculus for bisectorial Clifford operators 双向克利福德算子的 $H^infty$ 函数微积分
arXiv - MATH - Functional Analysis Pub Date : 2024-09-11 DOI: arxiv-2409.07249
Francesco Mantovani, Peter Schlosser
{"title":"The $H^infty$-functional calculus for bisectorial Clifford operators","authors":"Francesco Mantovani, Peter Schlosser","doi":"arxiv-2409.07249","DOIUrl":"https://doi.org/arxiv-2409.07249","url":null,"abstract":"The aim of this article is to introduce the H-infinity functional calculus\u0000for unbounded bisectorial operators in a Clifford module over the algebra R_n.\u0000While recent studies have focused on bounded operators or unbounded paravector\u0000operators, we now investigate unbounded fully Clifford operators and define\u0000polynomially growing functions of them. We first generate the omega-functional\u0000calculus for functions that exhibit an appropriate decay at zero and at\u0000infinity. We then extend to functions with a finite value at zero and at\u0000infinity. Finally, using a subsequent regularization procedure, we can define\u0000the H-infinity functional calculus for the class of regularizable functions,\u0000which in particular include functions with polynomial growth at infinity and,\u0000if T is injective, also functions with polynomial growth at zero.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space 论向量值哈迪空间上解析托普利兹算子的单元等价性和还原子空间
arXiv - MATH - Functional Analysis Pub Date : 2024-09-11 DOI: arxiv-2409.07112
Cui Chen, Yucheng Li, Ya Wang
{"title":"On unitary equivalence and reducing subspaces of analytic Toeplitz operator on vector-valued Hardy space","authors":"Cui Chen, Yucheng Li, Ya Wang","doi":"arxiv-2409.07112","DOIUrl":"https://doi.org/arxiv-2409.07112","url":null,"abstract":"In this paper, we proved that $T_{z^n}$ acting on the $mathbb{C}^m$-valued\u0000Hardy space $H_{mathbb{C}^m}^2(mathbb{D})$, is unitarily equivalent to\u0000$bigoplus_1^{mn}T_z$, where $T_z$ is acting on the scalar-valued Hardy space\u0000$H_{mathbb{C}}^2(mathbb{D})$. And using the matrix manipulations combined\u0000with operator theory methods, we completely describe the reducing subspaces of\u0000$T_{z^n}$ on $H_{mathbb{C}^m}^2(mathbb{D})$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"175 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity 遗传频繁超循环算子和不相连频繁超循环性
arXiv - MATH - Functional Analysis Pub Date : 2024-09-11 DOI: arxiv-2409.07103
F. Bayart, S. Grivaux, E. Matheron, Q. Menet
{"title":"Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity","authors":"F. Bayart, S. Grivaux, E. Matheron, Q. Menet","doi":"arxiv-2409.07103","DOIUrl":"https://doi.org/arxiv-2409.07103","url":null,"abstract":"We introduce and study the notion of hereditary frequent hypercyclicity,\u0000which is a reinforcement of the well known concept of frequent hypercyclicity.\u0000This notion is useful for the study of the dynamical properties of direct sums\u0000of operators; in particular, a basic observation is that the direct sum of a\u0000hereditarily frequently hypercyclic operator with any frequently hypercyclic\u0000operator is frequently hypercyclic. Among other results, we show that operators\u0000satisfying the Frequent Hypercyclicity Criterion are hereditarily frequently\u0000hypercyclic, as well as a large class of operators whose unimodular\u0000eigenvectors are spanning with respect to the Lebesgue measure. On the other\u0000hand, we exhibit two frequently hypercyclic weighted shifts $B_w,B_{w'}$ on\u0000$c_0(mathbb{Z}_+)$ whose direct sum $B_woplus B_{w'}$ is not\u0000$mathcal{U}$-frequently hypercyclic (so that neither of them is hereditarily\u0000frequently hypercyclic), and we construct a $C$-type operator on\u0000$ell_p(mathbb{Z}_+)$, $1le p<infty$ which is frequently hypercyclic but not\u0000hereditarily frequently hypercyclic. We also solve several problems concerning\u0000disjoint frequent hypercyclicity: we show that for every $Ninmathbb{N}$, any\u0000disjoint frequently hypercyclic $N$-tuple of operators $(T_1,dots ,T_N)$ can\u0000be extended to a disjoint frequently hypercyclic $(N+1)$-tuple $(T_1,dots\u0000,T_N, T_{N+1})$ as soon as the underlying space supports a hereditarily\u0000frequently hypercyclic operator; we construct a disjoint frequently hypercyclic\u0000pair which is not densely disjoint hypercyclic; and we show that the pair\u0000$(D,tau_a)$ is disjoint frequently hypercyclic, where $D$ is the derivation\u0000operator acting on the space of entire functions and $tau_a$ is the operator\u0000of translation by $ainmathbb{C}setminus{ 0}$. Part of our results are in\u0000fact obtained in the general setting of Furstenberg families.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Dyadic Approach to Weak Characterizations of Function Spaces 函数空间弱特征的二元方法
arXiv - MATH - Functional Analysis Pub Date : 2024-09-11 DOI: arxiv-2409.07395
Galia Dafni, Shahaboddin Shaabani
{"title":"A Dyadic Approach to Weak Characterizations of Function Spaces","authors":"Galia Dafni, Shahaboddin Shaabani","doi":"arxiv-2409.07395","DOIUrl":"https://doi.org/arxiv-2409.07395","url":null,"abstract":"Weak-type quasi-norms are defined using the mean oscillation or the mean of a\u0000function on dyadic cubes, providing discrete analogues and variants of the\u0000corresponding quasi-norms on the upper half-space previously considered in the\u0000literature. Comparing the resulting function spaces to known function spaces\u0000such as $dot{W}^{1,p}(rn)$, $JNp$, $Lp$ and weak-$Lp$ gives new embeddings\u0000and characterizations of these spaces. Examples are provided to prove the\u0000sharpness of the results.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Radon-Nikod$acute{Y}$m property of $mathbb{L}$-Banach spaces and the dual representation theorem of $mathbb{L}$-Bochner function spaces $mathbb{L}$-Banach 空间的 Radon-Nikod$acute{Y}$m 特性和 $mathbb{L}$-Bochner 函数空间的对偶表示定理
arXiv - MATH - Functional Analysis Pub Date : 2024-09-10 DOI: arxiv-2409.06279
Xia Zhang, Xiangle Yan, Ming Liu
{"title":"The Radon-Nikod$acute{Y}$m property of $mathbb{L}$-Banach spaces and the dual representation theorem of $mathbb{L}$-Bochner function spaces","authors":"Xia Zhang, Xiangle Yan, Ming Liu","doi":"arxiv-2409.06279","DOIUrl":"https://doi.org/arxiv-2409.06279","url":null,"abstract":"In this paper, we first introduce $mathbb{L}$-$mu$-measurable functions and\u0000$mathbb{L}$-Bochner integrable functions on a finite measure space\u0000$(S,mathcal{F},mu),$ and give an $mathbb{L}$-valued analogue of the\u0000canonical $L^{p}(Omega,mathcal{F},mu).$ Then we investigate the completeness\u0000of such an $mathbb{L}$-valued analogue and propose the Radon-Nikod$acute{y}$m\u0000property of $mathbb{L}$-Banach spaces. Meanwhile, an example constructed in\u0000this paper shows that there do exist an $mathbb{L}$-Banach space which fails\u0000to possess the Radon-Nikod$acute{y}$m property. Finally, based on above work,\u0000we establish the dual representation theorem of $mathbb{L}$-Bochner integrable\u0000function spaces, which extends and improves the corresponding classical result.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"317 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An analytic characterization of symbols of operators on non-Gaussian Mittag-Leffler functionals 非高斯 Mittag-Leffler 函数上算子符号的解析表征
arXiv - MATH - Functional Analysis Pub Date : 2024-09-10 DOI: arxiv-2409.06143
Wolfgang Bock, Ang Elyn Gumanoy, Sheila Menchavez, Elmira Nabizadeh Morsalfard
{"title":"An analytic characterization of symbols of operators on non-Gaussian Mittag-Leffler functionals","authors":"Wolfgang Bock, Ang Elyn Gumanoy, Sheila Menchavez, Elmira Nabizadeh Morsalfard","doi":"arxiv-2409.06143","DOIUrl":"https://doi.org/arxiv-2409.06143","url":null,"abstract":"In this paper, we provide proofs for the analytic characterization theorems\u0000of the operator symbols utilizing the characterization theorem for the\u0000Mittag-Leffler distribution space.We work out examples which can be interpreted\u0000as integral kernel operators and treat the important case of the translation\u0000operator.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups 在无穷维流形中取值的绝对连续函数的流形和半李群的正则特性
arXiv - MATH - Functional Analysis Pub Date : 2024-09-10 DOI: arxiv-2409.06512
Matthieu F. Pinaud
{"title":"Manifolds of absolutely continuous functions with values in an infinite-dimensional manifold and regularity properties of half-Lie groups","authors":"Matthieu F. Pinaud","doi":"arxiv-2409.06512","DOIUrl":"https://doi.org/arxiv-2409.06512","url":null,"abstract":"For $pin [1,infty]$, we define a smooth manifold structure on the set of\u0000absolutely continuous functions $gammacolon [a,b]to N$ with\u0000$L^p$-derivatives for each smooth manifold $N$ modeled on a sequentially\u0000complete locally convex topological vector space which admits a local addition.\u0000Smoothness of natural mappings between spaces of absolutely continuous\u0000functions is discussed. For $1leq p <infty$ and $rin mathbb{N}$ we show\u0000that the right half-Lie groups $text{Diff}_K(mathbb{R})$ and $text{Diff}(M)$\u0000are $L^p$-semiregular. Here $K$ is a compact subset of $mathbb{R}^n$ and $M$\u0000is a compact smooth manifold. For the preceding examples, the evolution map\u0000$text{Evol}$ is continuous.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximal hyperplane sections of the unit ball of $l_p$ for $p>2$ 在 $p>2$ 时，单位球 $l_p$ 的最大超平面截面
arXiv - MATH - Functional Analysis Pub Date : 2024-09-10 DOI: arxiv-2409.06432
Hermann König
{"title":"Maximal hyperplane sections of the unit ball of $l_p$ for $p>2$","authors":"Hermann König","doi":"arxiv-2409.06432","DOIUrl":"https://doi.org/arxiv-2409.06432","url":null,"abstract":"The maximal hyperplane section of the $l_infty^n$-ball, i.e. of the\u0000$n$-cube, is the one perpendicular to 1/sqrt 2 (1,1,0, ... ,0), as shown by\u0000Ball. Eskenazis, Nayar and Tkocz extended this result to the $l_p^n$-balls for\u0000very large $p ge 10^{15}$. We show that the analogue of Ball's result\u0000essentially holds for all $26.265 simeq p_0 le p < infty$. By Oleszkiewicz,\u0000Ball's result does not transfer to $l_p^n$ for $2 < p < p_0$. Then the\u0000hyperplane section perpendicular to the main diagonal yields a counterexample\u0000for large dimensions $n$. In this case, we give an asymptotic upper bound for\u0000$20 < p < p_0$.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
When is the Szlenk derivation of a dual unit ball another ball? 什么时候对偶单位球的 Szlenk 派生才是另一个球？
arXiv - MATH - Functional Analysis Pub Date : 2024-09-09 DOI: arxiv-2409.05516
Tomasz Kochanek, Marek Miarka
{"title":"When is the Szlenk derivation of a dual unit ball another ball?","authors":"Tomasz Kochanek, Marek Miarka","doi":"arxiv-2409.05516","DOIUrl":"https://doi.org/arxiv-2409.05516","url":null,"abstract":"We show that if a separable Banach space has Kalton's property $(M^ast)$,\u0000then all $varepsilon$-Szlenk derivations of the dual unit ball are balls,\u0000however, in the case of the dual of Baernstein's space, all those Szlenk\u0000derivations are balls having the same radius as for $ell_2$, yet this space\u0000fails property $(M^ast)$. By estimating the radii of enveloping balls, we show\u0000that the Szlenk derivations are not balls for Tsirelson's space and the dual of\u0000Schlumprecht's space. Using the Karush-Kuhn-Tucker theorem we prove that the\u0000same is true for the duals of certain sequential Orlicz spaces.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142208148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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