1 citations · 1 across the 4 of their papers we have counts for
6 papers · 1 filter
Weakly LUR norms and the Schur property
Szymon Draga, Tomasz Kania
A separable real or complex Banach space fails the Schur property if and only if it admits an equivalent Gâteaux smooth, weakly locally uniformly rotund norm which is not midpoint…
Operator ideals and three-space properties of asymptotic ideal seminorms
Ryan M. Causey, Szymon Draga, Tomasz Kochanek
We introduce asymptotic analogues of the Rademacher and martingale type and cotype of Banach spaces and operators acting on them. Some classical local theory results related, for e…
When is multiplication in a Banach algebra open?
Szymon Draga, Tomasz Kania
We develop the theory of Banach algebras whose multiplication (regarded as a bilinear map) is open. We demonstrate that such algebras must have topological stable rank 1, however t…
The Szlenk power type and tensor products of Banach spaces
Szymon Draga, Tomasz Kochanek
We prove a formula for the Szlenk power type of the injective tensor product of Banach spaces with Szlenk index at most . We also show that the Szlenk power type as well as summ…
Direct sums and summability of the Szlenk index
Szymon Draga, Tomasz Kochanek
We prove that the -sum of separable Banach spaces with uniformly summable Szlenk index has summable Szlenk index, whereas this result is no longer valid for more general direc…
On weakly locally uniformly rotund norms which are not locally uniformly rotund
Szymon Draga
We show that every infinite-dimensional Banach space with separable dual admits an equivalent norm which is weakly locally uniformly rotund but not locally uniformly rotund.