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Axioms
Special Issues
Recent Advances in Functional Analysis and Operator Theory
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Recent Advances in Functional Analysis and Operator Theory

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 9562

Special Issue Editors

Prof. Dr. Hadi Roopaei

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Guest Editor
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada
Interests: functional analysis; operator theory; real analysis; matrix theory
Prof. Dr. Feyzi Başar

E-Mail Website
Guest Editor
Department of Primary Mathematics Teacher Education, İnönü University, 44280 Malatya, Turkey
Interests: functional analysis; summability; sequence spaces; FK-spaces; bases; dual spaces; matrix transformations; spectrum, and the fine spectrum of a limitation matrix over any given sequence space; the Alpha-, Beta- and Gamma-duals and some topological properties of the matrix domains; sets of the sequences of fuzzy numbers; multiplicative calculus

Special Issue Information

Dear Colleagues, 

Functional analysis is a branch of mathematics that examines vector spaces with some sort of limit-related structure, as well as the linear functions corresponding to these spaces. An important branch of functional analysis is operator theory, which studies the properties of operators and how operators can be used to solve different problems. Mathematics’ operator concept evolved from classical analysis, such as integral equations and the solution of eigenfunctions and eigenvalues for differential operators, such as the Sturm–Liouville problem.

The operator theory is widely used in the solution of ordinary and partial differential equations and provides the mathematical framework for quantum mechanics. Mathematical physics, mechanical engineering and control engineering systems are some sciences that can benefit from the operator theory. 

Axioms intends to launch a Special Issue on functional analysis and the operator theory. This Issue will invite researchers to present their latest innovations, trends, concerns, practical challenges they have encountered and the solutions they have adopted in the area of operator theory. Original and unpublished mathematics papers with high standards of recent advances and significant implications are welcome in this Special Issue.  

Prof. Dr. Hadi Roopaei
Prof. Dr. Feyzi Başar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • norm of operators
  • bounded operators
  • compact operators
  • commutants of operators
  • special operators (Hausdorff, Hilbert, Cesaro, backward/forward difference operator, weighted mean, Norlund, L-matrices, etc.)
  • factorization of operators
  • composition of operators
  • spectrum of operators
  • sequence spaces
  • summability

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (8 papers)

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Research

20 pages, 326 KiB  
Article
Noncommutative Multi-Parameter Subsequential Wiener–Wintner-Type Ergodic Theorem
by Mu Sun and Yinmei Zhang
Axioms 2024, 13(9), 595; https://doi.org/10.3390/axioms13090595 - 31 Aug 2024
Viewed by 574
Abstract
This paper is devoted to the study of a multi-parameter subsequential version of the “Wiener–Wintner” ergodic theorem for the noncommutative Dunford–Schwartz system. We establish a structure to prove “Wiener–Wintner”-type convergence over a multi-parameter subsequence class Δ instead of the weight class case. In [...] Read more.
This paper is devoted to the study of a multi-parameter subsequential version of the “Wiener–Wintner” ergodic theorem for the noncommutative Dunford–Schwartz system. We establish a structure to prove “Wiener–Wintner”-type convergence over a multi-parameter subsequence class Δ instead of the weight class case. In our subsequence class, every term of k̲∈Δ is one of the three kinds of nonzero density subsequences we consider. As key ingredients, we give the maximal ergodic inequalities of multi-parameter subsequential averages and obtain a noncommutative subsequential analogue of the Banach principle. Then, by combining the critical result of the uniform convergence for a dense subset of the noncommutative Lp(M) space and the noncommutative Orlicz space, we immediately obtain the main theorem. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
10 pages, 268 KiB  
Article
Consistent Sampling Approximations in Abstract Hilbert Spaces
by Sinuk Kang, Kil Hyun Kwon and Dae Gwan Lee
Axioms 2024, 13(7), 489; https://doi.org/10.3390/axioms13070489 - 21 Jul 2024
Viewed by 545
Abstract
This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results [...] Read more.
This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
21 pages, 316 KiB  
Article
Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain
by Zhi-Jie Jiang
Axioms 2023, 12(12), 1131; https://doi.org/10.3390/axioms12121131 - 17 Dec 2023
Cited by 1 | Viewed by 1150
Abstract
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that [...] Read more.
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
15 pages, 333 KiB  
Article
Metrical Boundedness and Compactness of a New Operator between Some Spaces of Analytic Functions
by Stevo Stević
Axioms 2023, 12(9), 851; https://doi.org/10.3390/axioms12090851 - 31 Aug 2023
Viewed by 1109
Abstract
The metrical boundedness and metrical compactness of a new operator from the weighted Bergman-Orlicz spaces to the weighted-type spaces and little weighted-type spaces of analytic functions are characterized. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
11 pages, 307 KiB  
Article
Lp-Mapping Properties of a Class of Spherical Integral Operators
by Laith Hawawsheh, Ahmad Qazza, Rania Saadeh, Amjed Zraiqat and Iqbal M. Batiha
Axioms 2023, 12(9), 802; https://doi.org/10.3390/axioms12090802 - 22 Aug 2023
Cited by 3 | Viewed by 946
Abstract
In this paper, we study a class of spherical integral operators IΩf. We prove an inequality that relates this class of operators with some well-known Marcinkiewicz integral operators by using the classical Hardy inequality. We also attain the boundedness of [...] Read more.
In this paper, we study a class of spherical integral operators IΩf. We prove an inequality that relates this class of operators with some well-known Marcinkiewicz integral operators by using the classical Hardy inequality. We also attain the boundedness of the operator IΩf for some 1<p<2 whenever Ω belongs to a certain class of Lebesgue spaces. In addition, we introduce a new proof of the optimality condition on Ω in order to obtain the L2-boundedness of IΩ. Generally, the purpose of this work is to set up new proofs and extend several known results connected with a class of spherical integral operators. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
22 pages, 338 KiB  
Article
Bombieri-Type Inequalities and Their Applications in Semi-Hilbert Spaces
by Najla Altwaijry, Silvestru Sever Dragomir and Kais Feki
Axioms 2023, 12(6), 522; https://doi.org/10.3390/axioms12060522 - 26 May 2023
Cited by 1 | Viewed by 1138
Abstract
This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator A. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. [...] Read more.
This paper presents new results related to Bombieri’s generalization of Bessel’s inequality in a semi-inner product space induced by a positive semidefinite operator A. Specifically, we establish new inequalities that generalize the classical Bessel inequality and extend previous results in this area. Furthermore, our findings have applications to the study of operators on positive semidefinite inner product spaces, also known as semi-Hilbert spaces, and contribute to a deeper understanding of their properties and applications. Our work has implications for various fields, including functional analysis and operator theory. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
12 pages, 287 KiB  
Article
Norms of a Product of Integral and Composition Operators between Some Bloch-Type Spaces
by Stevo Stević
Axioms 2023, 12(5), 491; https://doi.org/10.3390/axioms12050491 - 18 May 2023
Viewed by 1027
Abstract
We present some formulas for the norm, as well as the essential norm, of a product of composition and an integral operator between some Bloch-type spaces of analytic functions on the unit ball, in terms of given symbols and weights. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
9 pages, 247 KiB  
Article
Norm of Hilbert Operator’s Commutants
by Hadi Roopaei
Axioms 2023, 12(5), 422; https://doi.org/10.3390/axioms12050422 - 26 Apr 2023
Viewed by 1232
Abstract
In this study, we obtain the ℓp-norms of six classes of operators that commute with the infinite Hilbert operators. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
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