15,492 research outputs found
The Dunford-Pettis property on tensor products
We show that, in some cases, the projective and the injective tensor products
of two Banach spaces do not have the Dunford-Pettis property (DPP). As a
consequence, we obtain that fails the DPP.
Since does enjoy it, this provides a new space
with the DPP whose dual fails to have it. We also prove that, if and
are -spaces, then has the DPP if
and only if both and have the Schur property. Other results and
examples are given.Comment: 9 page
Surjective factorization of holomorphic mappings
We characterize the holomorphic mappings between complex Banach spaces
that may be written in the form , where is another holomorphic
mapping and belongs to a closed surjective operator ideal.Comment: 8 page
The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces
We construct "higher" motion planners for automated systems whose space of
states are homotopy equivalent to a polyhedral product space
, e.g. robot arms with restrictions on the possible
combinations of simultaneously moving nodes. Our construction is shown to be
optimal by explicit cohomology calculations. The higher topological complexity
of other families of polyhedral product spaces is also determined.Comment: 30 pages. This second version of the paper extends the results of the
first version to the case of polyhedral product spaces
where no restriction is assumed on the sphere
dimensions $k_i
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