35 research outputs found
Duality on Banach spaces and a Borel parametrized version of Zippin's theorem
Let SB be the standard coding for separable Banach spaces as subspaces of
. In these notes, we show that if is
a Borel subset of spaces with separable dual, then the assignment can be realized by a Borel function . Moreover,
this assignment can be done in such a way that the functional evaluation is
still well defined (Theorem ). Also, we prove a Borel parametrized version
of Zippin's theorem, i.e., we prove that there exists and a
Borel function that assigns for each an isomorphic copy of
inside of (Theorem )
Operators whose dual has non-separable range
Let and be separable Banach spaces and be a bounded linear
operator. We characterize the non-separability of by means of fixing
properties of the operator .Comment: 20 pages, no figure
On pairs of definable orthogonal families
We introduce the notion of an M-family of infinite subsets of \nn which is
implicitly contained in the work of A. R. D. Mathias. We study the structure of
a pair of orthogonal hereditary families \aaa and \bbb, where \aaa is
analytic and \bbb is -measurable and an M-family.Comment: 21 pages, no figures. Illinois Journal of Mathematics (to appear
A classification of separable Rosenthal compacta and its applications
The present work consists of three parts. In the first one we determine the
prototypes of separable Rosenthal compacta and we provide a classification
theorem. The second part concerns an extension of a theorem of S. Todorcevic.
The last one is devoted to applications.Comment: 55 pages, no figure
Incomparable, non isomorphic and minimal Banach spaces
A Banach space contains either a minimal subspace or a continuum of
incomparable subspaces. General structure results for analytic equivalence
relations are applied in the context of Banach spaces to show that if
does not reduce to isomorphism of the subspaces of a space, in particular, if
the subspaces of the space admit a classification up to isomorphism by real
numbers, then any subspace with an unconditional basis is isomorphic to its
square and hyperplanes and has an isomorphically homogeneous subsequence