Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Factoring compact and weakly compact operators through reflexive Banach lattices


Authors: C. D. Aliprantis and O. Burkinshaw
Journal: Trans. Amer. Math. Soc. 283 (1984), 369-381
MSC: Primary 47B05; Secondary 47B55
MathSciNet review: 735429
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: When does a weakly compact operator between two Banach spaces factor through a reflexive Banach lattice?

This paper provides some answers to this question. One of the main results: If an operator between two Banach spaces factors through a Banach lattice with weakly compact factors, then it also factors through a reflexive Banach lattice. In particular, the square of a weakly compact operator on a Banach lattice factors through a reflexive Banach lattice.

Similar results hold for compact operators. For instance, the square of a compact operator on a Banach lattice factors with compact factors through a reflexive Banach lattice.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B05, 47B55

Retrieve articles in all journals with MSC: 47B05, 47B55


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0735429-0
Keywords: Weakly compact operators, factoring operators, reflexive Banach lattices
Article copyright: © Copyright 1984 American Mathematical Society