Recent Advances in Maps Preserving Problems and Algebraic Structures

Dear Colleagues,

Maps preserving problems play a fundamental role in algebra, operator theory, and functional analysis. These problems focus on characterizing mappings that maintain specific algebraic operations, such as Jordan triple products, Lie products, and other fundamental structures. Such mappings often reveal the deep structural properties of algebraic systems and have significant applications in various mathematical and applied fields. With the growing interplays between algebra and other disciplines, understanding preservers has become more important than ever.

On the one hand, structural preservation properties provide essential insights into the classification of algebras and their automorphisms, derivations, and homomorphisms. These results serve as a crucial foundation in many areas, including operator theory, non-associative algebra, and representation theory. On the other hand, perspectives from maps preserving problems can offer novel techniques for studying functional identities, stability analysis, and transformations in applied mathematics. This Special Issue will be devoted to state-of-the-art research on maps preserving problems and their connections with algebra, analysis, and other fields. The Guest Editors aim to provide a platform to present the latest advances in all aspects of maps preserving problems, from theoretical developments to practical applications.

Among the topics that this Special Issue will address, we may consider the following non-exhaustive list:

• Maps preserving Jordan triple products, Lie products, and other algebraic compositions;
• Preservers of functional identities, homomorphisms, isomorphisms, and derivations;
• Characterizations of algebraic and operator structures through preserving maps;
• Linear and non-linear preserver problems in prime and semiprime rings and algebras;
• Applications of preserving maps in operator theory, quantum mechanics, and functional analysis;
• New techniques and approaches for studying algebraic preservers.

We hope that this initiative will be attractive to researchers specialized in the above-mentioned fields. Contributions may be submitted on a continuous basis before the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.

Dr. Vahid Darvish
Prof. Dr. Cristina Flaut
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.

• maps preserving
• Jordan products
• Lie products
• homomorphisms
• derivations
• prime algebras
• von Neumann algebras
• structural characterizations