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Philip A. H. Brooker

- Research interests
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- The isomorphic theory of Banach spaces
- Banach algebras of operators on Banach spaces
Amongst the problems I find interesting are the following:
- 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.
- Email Address
- brookeratmaths.anu.edu.au
- Postal Address
- Centre for Mathematics and its Applications, Mathematical Sciences Institute
- Australian National University, Canberra, ACT 0200, Australia.
- Phone
- (61-2) 6125 4502
- FAX
- (61-2) 6125 5549
- Links
- Personal page
- The Banach Space Bulletin Board
- Banach Algebras 2007
- Biography of Stefan Banach
- Wikipedia entry on Banach spaces
- Australian
Mathematical Sciences Institute
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Mathematical Sciences Institute, ANU
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