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ON THE STRUCTURE OF THE SPREADING MODELS OF A BANACH G. ANDROULAKIS, E. ODELL, TH. SCHLUMPRECHT, N. TOMCZAK-JAEGERMANN
 

Summary: ON THE STRUCTURE OF THE SPREADING MODELS OF A BANACH
SPACE
G. ANDROULAKIS, E. ODELL, TH. SCHLUMPRECHT, N. TOMCZAK-JAEGERMANN
Abstract We study some questions concerning the structure of the set of spreading models
of a separable infinite-dimensional Banach space X. In particular we give an example of a
reflexive X so that all spreading models of X contain 1 but none of them is isomorphic to
1. We also prove that for any countable set C of spreading models generated by weakly null
sequences there is a spreading model generated by a weakly null sequence which dominates
each element of C. In certain cases this ensures that X admits, for each < 1, a spreading
model (~x
()
i )i such that if < then (~x
()
i )i is dominated by (and not equivalent to) (~x
()
i )i.
Some applications of these ideas are used to give sufficient conditions on a Banach space for
the existence of a subspace and an operator defined on the subspace, which is not a compact
perturbation of a multiple of the inclusion map.
1. Introduction

  

Source: Androulakis, George - Department of Mathematics, University of South Carolina

 

Collections: Mathematics