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ON THE STRUCTURE OF TENSOR PRODUCTS OF `p-SPACES Alvaro Arias
 

Summary: ON THE STRUCTURE OF TENSOR PRODUCTS OF `p-SPACES
by
Alvaro Arias
The University of Texas at San Antonio
and
Je D. Farmer
The University of Northern Colorado
Abstract. We examine some structural properties of (injective and projective) tensor
products of `p-spaces (projections, complemented subspaces, re exivity, isomorphisms,
etc.). We combine these results with combinatorial arguments to address the question of
primarity for these spaces and their duals.
This research was partially supported by NSF DMS{8921369.
Portions of this paper form a part of the second author's Ph.D. dissertation under
the supervision of W.B. Johnson. This research was also partially supported by NSF
DMS{8921369.
0
0. Introduction.
A Banach space X is prime if every in nite-dimensional complemented subspace con-
tains a further subspace which is isomorphic to X. A Banach space X is said to be primary
if whenever X = Y Z, X is isomorphic to either Y or Z. The classical examples of prime

  

Source: Arias, Alvaro - Department of Mathematics, University of Denver

 

Collections: Mathematics