Operator Theory and Related Topics

Dear Colleagues,

We are pleased to introduce this Special Issue, titled “Operator Theory and Related Topics”, which aims to synthesize recent contributions that reflect the vitality and diversity of current research in functional analysis and operator theory. These closely intertwined areas continue to develop rapidly, offering both deep theoretical advances and a wide range of applications across mathematics, physics, and engineering.

Functional analysis provides the underlying framework for the study of function spaces and the operators defined on them, while operator theory focuses on understanding the structure, spectrum, and behavior of such operators—particularly in Hilbert and Banach spaces. These tools are indispensable in modern mathematical analysis, with far-reaching applications in quantum mechanics, differential equations, control theory, and signal processing.

We invite researchers and scholars from around the world to contribute original research articles, comprehensive surveys, and brief communications that offer novel methods, refined techniques, or new connections between operator theory and other branches of mathematics. The objective of this issue is to create a space for high-level dialogue and the dissemination of results that may inspire future directions of inquiry.

Topics of interest include, but are not limited to, the following:

1. Operator inequalities and their applications;
2. Spectral theory of linear and nonlinear operators;
3. Functional analytic methods in mathematical physics and quantum theory;
4. Recent advances in Banach and Hilbert space operator theory;
5. Interdisciplinary applications of operator theory;
6. Generalizations and refinements of classical results in functional analysis;
7. Matrix inequalities and operator-theoretic interpretations;
8. Operator monotone and operator convex functions.

We are hopeful that this Special Issue will serve as a valuable reference for researchers and contribute meaningfully to the ongoing development of the field.

Dr. Cristian Conde
Guest Editor

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.

• spectral theory and spectral radius
• operator matrices and elementary operators
• orthogonality in operator spaces
• numerical ranges and norm inequalities
• unitarily invariant norms
• matrix inequalities and operator monotone functions
• orthogonal projections and positive operators
• perturbation theory and stability analysis
• functional calculus and operator algebras
• Banach and Hilbert space theory
• operator inequalities
• multivariable operator theory