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dc.contributor.advisorKhare, Apoorva
dc.contributor.advisorMisra, Gadadhar
dc.contributor.authorBose, Babhrubahan
dc.date.accessioned2024-04-12T05:39:47Z
dc.date.available2024-04-12T05:39:47Z
dc.date.submitted2024
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/6479
dc.description.abstractIn this thesis, we have tried to understand the geometry of normed spaces in the light of Birkhoff-James orthogonality. Using the first two chapters to give introductory notes and to establish relevant notations and terminologies, we have presented the work done in the following four chapters. In chapter three, we have studied the geometry of the normed algebra of holomorphic maps in a neighborhood of a curve and have established a relationship between the geometry of the algebra and the zeros of holomorphic maps. In the fourth chapter, we have studied Birkhoff-James orthogonality and its pointwise symmetry in Lebesgue spaces defined on arbitrary measure spaces and natural numbers. We have found the onto isometries of the sequence spaces using the symmetry of the aforementioned orthogonality. In the fifth chapter, we have studied the geometry of tensor product spaces and have used the results to study the relationship between the symmetry of orthogonality and the geometry (for example, extreme points) of certain spaces of operators. Our work in this chapter is motivated by the famous Grothendieck inequality. In the sixth and final chapter, we have studied the geometry of ℓp and c0 direct sums of normed spaces (1 ⩽ p <∞). We characterize the smoothness and approximate smoothness of these spaces along with Birkhoff-James orthogonality and its pointwise symmetry. As a consequence of our study, we have answered a question pertaining to the approximate smoothness of a space raised by Chmeili´enski, Khurana, and Sain in [14].en_US
dc.description.sponsorshipPrime Minister's Research Fellowship, ID: 0200182en_US
dc.language.isoen_USen_US
dc.relation.ispartofseries;ET00488
dc.rightsI grant Indian Institute of Science the right to archive and to make available my thesis or dissertation in whole or in part in all forms of media, now hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertationen_US
dc.subjectnormed spacesen_US
dc.subjectBirkhoff-James orthogonalityen_US
dc.subjectholomorphic mapsen_US
dc.subjecttensor product spacesen_US
dc.subject.classificationResearch Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis::Algebra and geometryen_US
dc.titleGeometry of normed linear spaces in light of Birkhoff-James orthogonalityen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.grantorIndian Institute of Scienceen_US
dc.degree.disciplineFaculty of Scienceen_US


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