Date of Submission

6-25-2025

Date of Award

2-25-2026

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Bangalore)

Supervisor

Nayak, Soumyashant (Indian Statistical Institute)

Abstract (Summary of the Work)

The classical Jordan–Chevalley decomposition expresses a matrix A ∈ Mn(C) as a unique commuting sum A = D + N, where D is diagonalizable and N is nilpotent. Although this decomposition is algebraic in origin, it encodes significant spectral information and, as shown by Nayak, has an important analytic consequence: the convergence of the normalized power sequence {|A^n|^ 1/n }n∈N ; |A| := (A∗A)^1/2 . In this thesis we study Jordan-Chevalley–type decompositions in infinite-dimensional settings and their connection with the convergence behaviour of normalized power sequences. In particular, we discuss this phenomenon for Dunford’s spectral operators and compact operators on a complex Hilbert space, and further extend the theory to operators affiliated with finite type I von Neumann algebras.

Control Number

TH684

DOI

https://dspace.isical.ac.in/items/1a8f722e-6cea-4e6c-b93b-6cffa7d0e5c3

DSpace Identifier

http://hdl.handle.net/10263/7665

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