Electronic Theses and Dissertations

Date

2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematical Sciences

Committee Chair

Bentuo Zheng

Committee Member

Irena Lasiecka

Committee Member

Roberto Triggiani

Committee Member

Anna Kaminska

Abstract

An important problem in Banach space theory since the 1950s has been the study of the structure of closed algebraic ideals in the algebra L (X ) where X is a Banach space.The Banach spaces X for which that structure is well-known are very few. It is known that every non-zero ideal in L (X ) contains the ideal of all finite-rank operators on X and that if X has a Schauder basis every non-zero closed ideal in L (X ) contains the ideal of all compact operators on X.In this dissertation I study the structure of the space (l_q)_c_0, for 1 < q < and I find the unique proper maximal ideal in the algebra L((l_q)_c_0).Let T be a bounded linear operator on X=(l_q)_c_0 with 1

Comments

Data is provided by the student.

Library Comment

Dissertation or thesis originally submitted to ProQuest

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