Advances in Operator Theory最新文献

Normality properties of Volterra-type integral operators on the Fock space Fock空间上volterra型积分算子的正态性

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Advances in Operator Theory Pub Date : 2026-10-21 DOI: 10.1007/s43036-026-00541-6

Tesfa Mengestie

引用次数: 0

Nearly invariant subspaces and weighted dual truncated Toeplitz operators 近不变子空间和加权对偶截断Toeplitz算子

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Advances in Operator Theory Pub Date : 2026-10-12 DOI: 10.1007/s43036-026-00539-0

Sudip Ranjan Bhuia

{"title":"Nearly invariant subspaces and weighted dual truncated Toeplitz operators","authors":"Sudip Ranjan Bhuia","doi":"10.1007/s43036-026-00539-0","DOIUrl":"10.1007/s43036-026-00539-0","url":null,"abstract":"<div>Let (mathcal {M}=hmathcal {K}_u) be a nearly (S^*)-invariant subspace of (H^2), where (mathcal {K}_u=H^2ominus uH^2) and h is the extremal multiplier. For (varphi in L^infty (mathbb {T})), we study the compression <div><div>$$ D_varphi ^mathcal {M}= P_{mathcal {M}^perp }M_varphi Big |_{mathcal {M}^perp }, $$</div></div>called a weighted dual truncated Toeplitz operator. When (hequiv 1), this reduces to the classical dual truncated Toeplitz operator.Using the Hartmann–Ross projection formula, we prove <div><div>$$ Vert D_varphi ^mathcal {M}Vert =Vert varphi Vert _infty , $$</div></div>characterize compactness, and show that the natural multiplication map by h identifies the weighted and classical theories precisely when h is inner. We also establish complex symmetry and obtain block matrix, defect, and semi-commutator identities via weighted truncated Hankel operators. As a main algebraic consequence, we prove <div><div>$$ D_varphi ^mathcal {M}D_psi ^mathcal {M}=0 quad Longleftrightarrow quad varphi =0 text {or} psi =0 quad text {a.e. on }mathbb {T}. $$</div></div>Finally, we derive a rank-at-most-two correction formula and a finite-rank displacement identity for the generalized dual shift (D_z^mathcal {M}).</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188994","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 the extension of EP and Hypo-EP operators 关于EP算子和拟EP算子的扩展

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Advances in Operator Theory Pub Date : 2026-10-01 DOI: 10.1007/s43036-026-00535-4

R. Semmami, H. Ezzahraoui, E. H. Zerouali

引用次数: 0

Indeterminate Jacobi operators II 不定Jacobi算子II

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Advances in Operator Theory Pub Date : 2026-09-28 DOI: 10.1007/s43036-026-00537-2

Christian Berg, Ryszard Szwarc

引用次数: 0

Quantitative Menshov-type universal series for bounded Vilenkin systems with (ell ^q) coefficients, (q>2) 具有(ell ^q)系数的有界Vilenkin系统的定量menshov型泛级数 (q>2)

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Advances in Operator Theory Pub Date : 2026-09-24 DOI: 10.1007/s43036-026-00538-1

S. A. Episkoposian

{"title":"Quantitative Menshov-type universal series for bounded Vilenkin systems with (ell ^q) coefficients, (q>2)","authors":"S. A. Episkoposian","doi":"10.1007/s43036-026-00538-1","DOIUrl":"10.1007/s43036-026-00538-1","url":null,"abstract":"<div>Let (m=(m_1,m_2,ldots )) be a bounded generating sequence, (2le m_nle Lambda <infty ), and let ({psi _j}_{jge 0}) be the associated Vilenkin system. For every fixed (q>2), we construct a formal Vilenkin series with coefficients in (ell ^q) whose ordinary partial sums have a uniform exceptional-set universality property. Precisely, for every (varepsilon >0) there exists a measurable set (E_varepsilon subset [0,1)) with (operatorname {mes}E_varepsilon <varepsilon ), chosen independently of both the exponent p and the target g, such that for every (1le p<infty ) and every (gin L^p[0,1)) there is a subsequence of the ordinary partial sums, allowed to depend on p and g, which converges to g in (L^p([0,1)setminus E_varepsilon )). The proof is based on a quantitative localization lemma: from an m-adic step function and a prescribed initial spectral index we construct a high-frequency Vilenkin polynomial which reproduces the function outside a small set and has arbitrarily small (ell ^q) coefficient mass. The required multiplier is selected probabilistically on a finite abelian digit group. We also distinguish two endpoint phenomena at (q=2): Parseval’s identity obstructs the particular finite-block multiplier mechanism in (ell ^2), whereas the Riesz–Fischer theorem rules out the stated global universality property for every (ell ^2) coefficient sequence.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035082","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

K–g-fusion frame generators for unitary systems on Hilbert spaces Hilbert空间上酉系统的k - g融合系生成

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Advances in Operator Theory Pub Date : 2026-09-17 DOI: 10.1007/s43036-026-00536-3

Jingyan Zhang, Xunxiang Guo

{"title":"K–g-fusion frame generators for unitary systems on Hilbert spaces","authors":"Jingyan Zhang, Xunxiang Guo","doi":"10.1007/s43036-026-00536-3","DOIUrl":"10.1007/s43036-026-00536-3","url":null,"abstract":"<div>K–g-fusion frame is a generalization of several currently popular frames, including the fusion frames, K-fusion frames and g-fusion frames. And structured frames are one of most interest current research subjects. In this paper, we mainly study structured K–g-fusion frames, i.e. K–g-fusion frames generated by an operator-space pair through a unitary system. We call such pair a K–g-fusion frame generator of the unitary system. We study some properties of K–g-fusion frame generators, which shows that under some condition we can obtain K–g-fusion frame generators by some simple ways. Moreover, under some condition we characterize K–g-fusion frame generators in terms of complete wandering subspaces and generalized local commutants. Finally, we discuss the duals of a K–g-fusion frame generator, which is called K–g-fusion dual Bessel generator of the generator. And under some weak condition, we completely characterize the structure of all K–g-fusion dual Bessel generators for a Parseval K–g-fusion frame generator and give an explicit construction of the canonical K–g-fusion dual Bessel generator for a Parseval K–g-fusion frame generator. Moreover, we show that under certain condition, existence of dual on range of K guarantees a K–g-fusion Bessel generator to be a K–g-fusion frame generator, and we also can generate a K–g-fusion frame generator from a K–g-fusion dual Bessel generator.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986733","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

Variational construction and spectral stability of hybrid Laplacians on heterogeneous media 异质介质上杂交拉普拉斯子的变分结构和谱稳定性

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Advances in Operator Theory Pub Date : 2026-09-11 DOI: 10.1007/s43036-026-00532-7

Marwa Ennaceur, Ahmed Hachani

{"title":"Variational construction and spectral stability of hybrid Laplacians on heterogeneous media","authors":"Marwa Ennaceur, Ahmed Hachani","doi":"10.1007/s43036-026-00532-7","DOIUrl":"10.1007/s43036-026-00532-7","url":null,"abstract":"<div>We construct a self-adjoint Laplacian on a heterogeneous medium coupling a bounded Lipschitz open set (Omega subset mathbb {R}^n) to a finite weighted graph (G=(V,E)), through the closed symmetric bilinear form <div><div>$$begin{aligned} mathcal {E}_varepsilon (u,u)&= Vert nabla u_cVert _{L^2(Omega )}^2 + sum _{iin V}kappa _i,|(A_varepsilon u_c)(i)-u_d(i)|^2&quad + sum _{{i,j}in E}w_{ij},|u_d(i)-u_d(j)|^2, end{aligned}$$</div></div>where (A_varepsilon ) averages (u_c) over a ball of radius (varepsilon ) at each coupling point; Kato’s representation theorem supplies the generator (L_varepsilon ). We study the limit (varepsilon downarrow 0). In dimension (n=1) the coupling survives: we prove Mosco, norm resolvent and spectral convergence with multiplicities, for finite coupling strengths and in the constrained regime (kappa _irightarrow +infty ). In every dimension (nge 2) it does not: for any coupling strengths whatsoever, including the capacity rescalings suggested by point-interaction heuristics, the forms converge to the fully decoupled one, singletons having zero (H^1)-capacity, so that the coupling constraint costs asymptotically no energy. The dichotomy governing the model is thus (n=1) against (nge 2), not the (nle 3) against (nge 4) of point-interaction theory. An analytical study and three finite-element experiments illustrate both regimes.</div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927638","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 operators commuting with a quasinilpotent operator of finite nullity and ascent 关于算子与有限零和有限上升的拟幂算子的可交换

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Advances in Operator Theory Pub Date : 2026-08-28 DOI: 10.1007/s43036-026-00534-5

Pietro Aiena, Miloš D. Cvetković

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Factorization of anti-linear and C-normal operators 反线性和c -正规算子的分解

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Advances in Operator Theory Pub Date : 2026-08-27 DOI: 10.1007/s43036-026-00533-6

Sudip Ranjan Bhuia

引用次数: 0

Jump type problems for inframonogenic functions on domains with fractal boundaries 分形边界域上次致函数的跳跃型问题