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Functional Analysis, Topology and Quantum Mechanics, 3rd Edition
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Functional Analysis, Topology and Quantum Mechanics, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".

Deadline for manuscript submissions: 31 July 2025 | Viewed by 2942

Special Issue Editors

Prof. Dr. Francisco Javier Garcia-Pacheco

E-Mail Website
Guest Editor
Department of Mathematics, College of Engineering, Universidad de Cádiz, 11510 Puerto Real, Spain
Interests: functional analysis; algebra; geometry; topology
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Rafael de la Rosa Silva

E-Mail Website
Guest Editor
Department of Mathematics, Universidad de Cádiz, 11510 Puerto Real, Cadiz, Spain
Interests: Lie symmetries; partial differential equations; nonlocal symmetries
Prof. Dr. José María Sánchez Delgado

E-Mail Website
Guest Editor
Department of Mathematics, Universidad de Cádiz, 11510 Puerto Real, Cadiz, Spain
Interests: Lie theory

Special Issue Information

Dear Colleagues,

The scope of this Special Issue deals with the strong interaction between the operator theory and the geometry of Banach spaces and topological vector spaces. Applications of the two aforementioned theories to quantum systems are very welcome. Moreover, this Special Issue deals with partial differential equations and algebraic structures that govern physical phenomena, especially, quantum mechanics phenomena.

Prof. Dr. Francisco Javier Garcia-Pacheco
Prof. Dr. Rafael de la Rosa Silva
Prof. Dr. José María Sánchez Delgado
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • banach spaces and algebras
  • Hilbert spaces
  • Selfadjoint operator
  • convexity and smoothness
  • algebras of continuous functions
  • measure spaces
  • non-associative algebras
  • Lie algebras
  • effect algebras
  • series and summability
  • poisson algebras
  • partial differential equations
  • quantum systems
  • probability density operator
  • unbounded observables

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Related Special Issues

Published Papers (4 papers)

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Research

34 pages, 498 KiB  
Article
Tensorial Maclaurin Approximation Bounds and Structural Properties for Mixed-Norm Orlicz–Zygmund Spaces
by Waqar Afzal, Mujahid Abbas, Mutum Zico Meetei and Saïd Bourazza
Mathematics 2025, 13(6), 917; https://doi.org/10.3390/math13060917 - 10 Mar 2025
Cited by 1 | Viewed by 440
Abstract
This article explores two distinct function spaces: Hilbert spaces and mixed-Orlicz–Zygmund spaces with variable exponents. We first examine the relational properties of Hilbert spaces in a tensorial framework, utilizing self-adjoint operators to derive key results. Additionally, we extend a Maclaurin-type inequality to the [...] Read more.
This article explores two distinct function spaces: Hilbert spaces and mixed-Orlicz–Zygmund spaces with variable exponents. We first examine the relational properties of Hilbert spaces in a tensorial framework, utilizing self-adjoint operators to derive key results. Additionally, we extend a Maclaurin-type inequality to the tensorial setting using generalized convex mappings and establish various upper bounds. A non-trivial example involving exponential functions is also presented. Next, we introduce a new function space, the mixed-Orlicz–Zygmund space ℓq(·)logβLp(·), which unifies Orlicz–Zygmund spaces of integrability and sequence spaces. We investigate its fundamental properties including separability, compactness, and completeness, demonstrating its significance. This space generalizes the existing structures, reducing to mixed-norm Lebesgue spaces when β=0 and to classical Lebesgue spaces when q=∞,β=0. Given the limited research on such spaces, our findings contribute valuable insights to the functional analysis. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics, 3rd Edition)
24 pages, 344 KiB  
Article
Localization and Flatness in Quantale Theory
by George Georgescu
Mathematics 2025, 13(2), 227; https://doi.org/10.3390/math13020227 - 11 Jan 2025
Viewed by 571
Abstract
The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales. The first question we must address is the definition of a [...] Read more.
The study of flat ring morphisms is an important theme in commutative algebra. The purpose of this article is to develop an abstract theory of flatness in the framework of coherent quantales. The first question we must address is the definition of a notion of “flat quantale morphism” as an abstraction of flat ring morphisms. For this, we start from a characterization of the flat ring morphism in terms of the ideal residuation theory. The flat coherent quantale morphism is studied in relation to the localization of coherent quantales. The quantale generalizations of some classical theorems from the flat ring morphisms theory are proved. The Going-down and Going-up properties are then studied in connection with localization theory and flat quantale morphisms. As an application, characterizations of zero-dimensional coherent quantales are obtained, formulated in terms of Going-down, Going-up, and localization. We also prove two characterization theorems for the coherent quantales of dimension at most one. The results of the paper can be applied both in the theory of commutative rings and to other algebraic structures: F-rings, semirings, bounded distributive lattices, commutative monoids, etc. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics, 3rd Edition)
14 pages, 288 KiB  
Article
Convergence of Implicit Iterative Processes for Semigroups of Nonlinear Operators Acting in Regular Modular Spaces
by Wojciech M. Kozlowski
Mathematics 2024, 12(24), 4007; https://doi.org/10.3390/math12244007 - 20 Dec 2024
Viewed by 370
Abstract
This paper focuses on one-parameter semigroups of ρ-nonexpansive mappings Tt:C→C, where C is a subset of a modular space Xρ, the parameter t ranges over [0,+∞), and ρ [...] Read more.
This paper focuses on one-parameter semigroups of ρ-nonexpansive mappings Tt:C→C, where C is a subset of a modular space Xρ, the parameter t ranges over [0,+∞), and ρ is a convex modular with the Fatou property. The common fixed points of such semigroups can be interpreted as stationary points of a dynamic system defined by the semigroup, meaning they remain unchanged during the transformation Tt at any given time t. We demonstrate that, under specific conditions, the sequence {xk} generated by the implicit iterative process xk+1=ckTtk+1(xk+1)+(1−ck)xk is ρ-convergent to a common fixed point of the semigroup. Our findings extend existing convergence results for semigroups of operators, from Banach spaces to a broader class of regular modular spaces. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics, 3rd Edition)
8 pages, 1320 KiB  
Article
C-Semigroups and Their Induced Order
by Daniel Marín-Aragón and Raquel Tapia-Ramos
Mathematics 2024, 12(18), 2889; https://doi.org/10.3390/math12182889 - 16 Sep 2024
Viewed by 888
Abstract
Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|<+∞. This structure has always been studied using a monomial order. The main issue [...] Read more.
Let C⊂Np be an integer polyhedral cone. An affine semigroup S⊂C is a C-semigroup if |C∖S|<+∞. This structure has always been studied using a monomial order. The main issue is that the choice of these orders is arbitrary. In the present work, we choose the order given by the semigroup itself, which is a more natural order. This allows us to generalise some of the definitions and results known from numerical semigroup theory to C-semigroups. Full article
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics, 3rd Edition)
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