## Electronic Theses and Dissertations

#### Date

2020

#### Date of Award

2020

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy

#### 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

#### Library Comment

Dissertation or thesis originally submitted to ProQuest

#### Recommended Citation

Calle Cadavid, Diego, "UNIQUE MAXIMAL IDEAL IN THE ALGEBRA L (( l_q)_c_0 ) WITH 1 < q " (2020). *Electronic Theses and Dissertations*. 2486.

https://digitalcommons.memphis.edu/etd/2486

## Comments

Data is provided by the student.