Functional Analysis & Operator Theory
Main Focus of Research Interests
The research area is focused on several topics in Functional Analysis, Operator Theory, Dynamical Systems and applications to Approximation Theory and Fixed Point Theory.
Weekly seminars are conducted on a regular basis where the newest results in the area are presented by faculty members, visitors, and graduate students. All faculty and graduate students are invited. Seminars can be found on News & Events page.
In the department, a number of doctoral degrees have been awarded in this area, and currently several Ph.D. students are working on their doctoral dissertation under the guidance of members of this group. The placement of Ph.D. students advised by the members of this group consists of research universities and colleges in the USA and abroad.
Below are research interests and three representative or recent publications from each member.Fernanda Botelho, Professor; Graduate Coordinator (Mathematics)
Research Interests: Representations for surjective isometries and hermitian operators on vector valued function spaces. Characterization of generalized bi- circular projections on several Banach spaces. Algebraic and topological properties of sets of operators. Dynamical Systems.
- Surjective isometries on Grassman spaces, Journal of Functional Analysis, 265(10), 2226-2238, with J. Jamison and L. Molnár), (2013).
- Hermitian operators on Lipschitz function spaces, Studia Mathematica, 215(2), 127-137, with J. Jamison, A. Jiménez- Vargas, and M. Villegas-Vallecillos, (2013).
- Homomorphisms on a class of commutative Banach algebras, Rocky Mountain Journal of Mathematics, 43(2), 395-416, with J. Jamison, (2013).
Research Interests: Isometric and isomorphic geometry of Banach spaces and locally bounded linear topological spaces, structural properties of Köthe and rearrangement invariant spaces, Orlicz spaces, Lorentz spaces, noncommutative spaces of measurable operators with applications to the best approximation and fixed point theory.
- Isomorphic copies in the lattice E and its symmetrization E(*) with applications to Orlicz-Lorentz spaces, Journal of Functional Analysis, 257, 271-331, with Yves Raynaud, (2009).
- Smooth points in symmetric spaces of measurable operators, Positivity, 16(1), 29-51, with M. Czerwińska and D. Kubiak, (2012).
- The Daugavet property in rearrangement invariant spaces, to appear in Transactions of Amer. Math. Soc., with M. Acosta and M.Mastyło
Research Interests: Geometry of Banach spaces, best approximation, fixed point property of nonexpansive mappings.
- Fixed point theory and nonexpansive mappings, Arab. J. Math. (Springer), 1(4), 495-509, (2012).
- Isometric shifts on (c ⊕ X)∞, J. Math. Anal. Appl., 384(2), 198-203, (2011).
- There is an equivalent norm on l1 that has the fixed point property, Nonlinear Anal., 68(8), 2303-2308, (2008).
Research Interests: Isomorphic theory of Banach spaces and its applications to frame theory, non-linear functional analysis, and approximation properties.
- A characterization of subspaces and quotients of reflexive Banach spaces with unconditional basis, Duke Mathematical Journal, 141(3), 505-518, with W. B. Johnson, (2008).
- Systems formed by translates of one element in Lp(R), Transactions of the American Mathematical Society, 363(12), 6505-6529, with E. Odell, B. Sari, and Th. Schlumprecht, (2011).
- The strong approximation property and the weak bounded approximation property, accepted by Journal of Functional Analysis, with J. Kim.