Spectral theory using operator algebra techniques.

Title: Spectral theory using operator algebra techniques.
Identifier: AAI9130357
identifier: 9130357
Creator: Paliogiannis, Fotios Constantinou.
Contributor: Adviser: Stanley Kaplan
Date: 1991
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In this work, we study the Spectral Theorem (the Functional calculus as well) for self adjoint and normal operators, both in the bounded and unbounded cases. The approach, to this structure theorem, is based on the following key theorem: Theorem: The Gelfand (or Structure) space of an abelian von Neumann algebra on a Hilbert space H, is extremely disconnected. The idea goes back to the (1952) paper of M. G. Fell and J. L. Kelley An algebra of unbounded Operators Proc. Nat. Acad. Sci. USA 38 592-598. R. V. Kadison and J. R. Ringrose discuss the spectral theorem from this point of view in their (1983) book Chap. 5 Vol. I. Our development is strongly suggested by this discussion, although our approach and proofs differ. Our proofs incorporate several ideas tying together function theory and operator theory.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.