activity
20102016
most citedDirect sums and the Szlenk index

13 citations · 18 across the 6 of their papers we have counts for

collaborators

7 papers

math.FA2016★ 3 cited

Non-Asplund Banach spaces and operators

Philip A. H. Brooker

Let and be Banach spaces such that is separable and let be a (continuous, linear) operator. We study consequences of the adjoint operator $R^\ast…

math.FA2016★ 2 cited

Absolutely convex sets of large Szlenk index

Philip A. H. Brooker

Let be a Banach space and an absolutely convex, weak-compact subset of . We study consequences of having a large or undefined Szlenk index and subsequent…

math.FA2012

Szlenk and -dentability indices of the Banach spaces

Philip A. H. Brooker

Let be an infinite ordinal and the unique ordinal satisfying . We show that the Banach space of all continuous scalar-valued functi…

math.FA2012

Three-space property for asymptotically uniformly smooth renormings

P. A. H. Brooker, G. Lancien

We prove that if is a closed subspace of a Banach space such that and admit an equivalent asymptotically uniformly smooth norm, then also admits an equivalent…

math.FA2010

Asplund operators and the Szlenk index

Philip A. H. Brooker

For an ordinal, we investigate the class consisting of all operators whose Szlenk index is an ordinal not exceeding . We show that each class $\mathscr{SZ…

math.FA2010★ 13 cited

Direct sums and the Szlenk index

Philip A. H. Brooker

For an ordinal and , we determine a necessary and sufficient condition for an -direct sum of operators to have Szlenk index not exceeding . It follows…

math.FA2010

Operator ideals associated with the Szlenk index

Philip A. H. Brooker

For an ordinal, we investigate the class consisting of all operators whose Szlenk index is an ordinal not exceeding . Our main result is that $\mathscr{SZ…