Philip A. H. Brooker

most citedDirect sums and the Szlenk index

13 citations · 13 across the 2 of their papers we have counts for

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2 papers

math.FA2010★ 13 cited

Direct sums and the Szlenk index

Philip A. H. Brooker

For $α$ an ordinal and $1 < p < \infty$ , we determine a necessary and sufficient condition for an $ℓ_{p}$ -direct sum of operators to have Szlenk index not exceeding $ω^{α}$ . It follows…

math.FA2010

Operator ideals associated with the Szlenk index

Philip A. H. Brooker

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