Date of Award
1-1-2024
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
First Advisor
Qingying Bu
Second Advisor
Gerard Buskes
Third Advisor
Samuel T. Lisi
Relational Format
dissertation/thesis
Abstract
Let E be an atomic reflexive Banach lattice and X be any Banach lattice.
In chapter 3, we study the inheritance of Pełczyński’s property (V) from E and X to their positive projective tensor product Eˆ⊗|π|X and positive injective tensor project Eˇ⊗|ε|X. In section 3.2, we show that Eˆ⊗|π|X has Pełczyński’s property (V) if and only if X has Pełczyński’s property (V) and every positive linear operator from E to X∗ is compact. In section 3.3, we show that Eˇ⊗|ε|X has Pełczyński’s property (V) if and only if X has Pełczyński’s property (V). In section 3.4, as an application, we provide new examples of non-reflexive Banach lattices with Pełczyński’s property (V).
In chapter 4, we study the inheritance of Pełczyński’s property (V∗) from E and X to their positive projective tensor product Eˆ⊗|π|X and positive injective tensor project Eˇ⊗|ε|X. In section 4.2, we show that Eˆ⊗|π|X has Pełczyński’s property (V∗) if and only if X has Pełczyński’s property (V∗). In section 4.3, we show that Eˇ⊗|ε|X has Pełczyński’s property (V∗) if and only if X has Pełczyński’s property (V∗) and every positive linear operator from E∗ to X is compact. In section 4.4, as an application, we provide new examples of non-reflexive Banach lattices with Pełczyński’s property (V∗).
Recommended Citation
Mate, Apoorva, "Pełczyński’s Properties (V) and (V∗) on Positive Tensor Products of Banach Lattices" (2024). Electronic Theses and Dissertations. 2838.
https://egrove.olemiss.edu/etd/2838