In matrix theory, functional analysis, and operator theory, the study of those (linear) mappings preserving ranks, spectra, spectral radii, numerical ranges, numerical radii, orthogonality or disjointness, respectively, has a long and distinguished history. There has been a great deal of active research conducted by different research groups around the world. A subject search on “numerical range,” “numerical radius,” or “field of values” on the MathSciNet will return over 1000 items. There are monographs, special issues of research journals, and chapters of textbooks devoted to the subject. Research papers on the subject appear regularly in reputed mathematical journals. Talks on the subject are frequently presented in mathematical conferences. Recently, researchers are also interested in similar problems in operator algebras, C*- and von Neumann algebras, and Jordan structures.

In view of the recent rapid development of the interrelationship among preserver problems of operator algebras, operator theory, and quantum information sciences, it was felt that a special issue on preserver problems should be published. Similar issues have been published before by other respectable mathematics journals, but the themes are sometimes in favor of matrix theory or operator algebras. We think that a new one with more emphasis on the function space aspects will be welcomed. In fact, many preserver problems in matrix theory, operator algebras, and functional analysis are related to those in function spaces, though, for example, functional calculus. It is the time to call for a more systematic approach based on function space techniques.

We invite original research articles as well as review articles describing the recent advances in preserver problems of function spaces and operator algebras. Papers of related topics are also welcomed. Potential topics include, but are not limited to:

• Linear and nonlinear maps between function spaces and operator algebras which preserve norms, positivity, orthogonality, disjointness, ranks, spectra, spectral radii, numerical ranges/radii, zero of polynomials, or some other special relations
• Algebraic and/or geometric structures of Banach spaces, function spaces, and operator algebras characterizing the structure of the original spaces or algebras
• Preserver problems in mathematical physics and quantum information theory
• General theory of Banach and function spaces and operator algebras, and the transformations between them, for example, fixed point theorems
• Other related problems of general interests

Before submission authors should carefully read over the journal’s Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/aaa/ppfs/ according to the following timetable: