Philip A. H. Brooker

• The isomorphic theory of Banach spaces
• Banach algebras of operators on Banach spaces

• The problem of determining the lattice of two-sided closed ideals in the Banach algebra L(X) of all bounded linear operators on a given Banach space X. More specifically, we would like to know all the closed ideals in L(X) and how they are related by set inclusion. The list of Banach spaces for which this problem has been fully solved is quite small.

• The Complemented Subspace Problem for Banach spaces. The CSP is stated as follows: Given a Banach space X, classify, up to isomorphism, all the infinite dimensional complemented subspaces of X.

• Ordinal indices of Banach spaces.

• Operators to and from C(K) spaces.

My supervisor is Rick Loy.