Document Type
Lecture
Publication Date
11-12-2008
Abstract
Let �� ⊗ �� denote the injective tensor product of Banach spaces �� and ��. (a) Suppose that either �� or �� has the Radon-Nikodym property and that either ��** or ��** has the approximation property. If both �� and �� have the Grothendieck property and each continuous linear operator from ��* to ��** is compact, then �� ⊗ �� has the Grothendieck property. (b) Suppose that �� is a reflexive space with an unconditional finite-dimensional decomposition and �� has the Grothendieck property. Then �� ⊗ �� has the Grothendieck property if and only if each continuous linear operator from ��* to �� is compact.
Relational Format
presentation
Recommended Citation
Bu, Qingying, "The Grothendieck Property for Injective Tensor Products" (2008). Analysis Seminar. 39.
https://egrove.olemiss.edu/math_analysis/39
