Ph.D. Thesis : Birkhoff-James orthogonality and distance formulas in C*-algebras and for tuples of operators
This thesis was devoted to the study of Birkhoff-James orthogonality in C*-algebras and its applications in finding some distance formulas. We had found a non-commutative analogous of the known characterizations of Birkhoff-James orthogonality. We had shown the applications of our results in the geometry of Banach spaces and discussed the connections of orthogonality characterizations and distance problems. We also provided a distance formula in terms of variance of tuples of operators. The thesis can be found on https://www.doi.org/10.13140/RG.2.2.20848.74247/1
Selected Invited and Contributory Presentations
August 7--11, 2023: Contributory presentation in Young Mathematicians in C*-Algebras (YMC*A 2023), KU Leuven, Belgium.
Title: Sequence of operator algebras converging to odd spheres in the quantum Gromov-Hausdorff distance, KU Leuven Presentation
11 November, 2022: Analysis Probability Research Group (APRG) Seminar, Indian Institute of Science(IISc).
Title: Sequence of Toeplitz algebras converge to odd spheres for the quantum Gromov-Hausdorff distance, IISc Presentation
10 September, 2022: 2022 Fall Matrix Seminar, University of Nevada, Reno, USA.
Title: Interpolation polynomials and linear algebra, UNR Presentation
April 6--9, 2022: Contributory talk in ILAS Special Session on Matrix Analysis and Applications II, Virtual JMM 2022, Meetings and Conference Department, American Mathematical Society.
Title: A distance formula for tuples of doubly commuting matrices, JMM 2022 Presentation
June 14--18, 2021: Contributory talk in Graduate Summer School in Operator Algebras (online), Fields Institute and the University of Ottawa,
Title: Orthogonality and Gateaux derivative of C*-norm, University of Ottawa Presentation