Walden Freedman
My research interests are mostly in Banach space theory.
Publications
6. Convergence preserving mappings on topological groups (submitted for publication in Topology and its Applications)
5. When does a quadratic extension field contain (the square root of -1)?, College Math Journal, 35, no. 1, (2004), p. 52-54
4. An extension property for Banach spaces, Colloquium Mathematicum, 91, no. 2, (2002), p. 167-182
A Banach space X has property (E) if every operator from X into c_0 extends to an operator from X** into c_0; X has
property (L) if whenever K is a bounded subset of X which is limited in X**, then K is limited in X; the space X has property
(G) if whenever K is a bounded subset of X which is a Grothendieck subset of X**, then K is a Grothendieck subset of X.
In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric
properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of
being a Grothendieck space.3. The Phillips properties, (with Ali Ulger) Proceedings of the AMS, 128 (7) (2000), p. 2137-2145.
A Banach space X has the Phillips property if the canonical projection from X*** onto X* is sequentially weak*-norm
continuous, and has the weak Phillips property if it is sequentially weak*-weak continuous. We study both properties
in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski's properties (u) and (V),
and the Schur property. Available at http://www.ams.org/proc/2000-128-07/S0002-9939-00-05703-8/S0002-9939-00-05703-8.pdf2. Alternative polynomial and holomorphic Dunford-Pettis properties, Turk. J. Math., 23, no. 3, (1999), p. 407-415.
Two alternatives to the Polynomial Dunford-Pettis Property and the Holomorphic Dunford-Pettis Property,
called the PDP1 and HDP1 properties, respectively, are introduced. Just as the Polynomial Dunford-Pettis
Property and Holomorphic Dunford-Pettis Property are known to be equivalent to the Dunford-Pettis Property,
it is shown that the PDP1 and HDP1 properties are similarly equivalent to the DP1 property introduced by the
author in a previous paper. Available at http://journals.tubitak.gov.tr/math/issues/mat-99-23-3/mat-23-3-6-9901-11.pdf1. An Alternative Dunford-Pettis property, Studia Mathematica 125, no. 2, (1997), p. 143-159.
An alternative to the Dunford-Pettis property, called the DP1 property, is introduced. Its relationship to the
Dunford-Pettis property and other related properties is examined. Conditions are given under which direct
sums of spaces with the DP1 property have the DP1 property. It is also shown that for preduals of von Neumann
algebras, DP1 is strictly weaker than the Dunford-Pettis property, while for von Neumann algebras, the two
properties are equivalent.
Phone: (707) 826-4763 Fax: (707) 826-3140 Click here to send me email!