Universal mappings for certain classes of operators and polynomials between Banach spaces

Raffaella Cilia and Joaquín M. Gutiérrez

Mathematische Nachrichten, 2017, vol. 290, issue 17-18, 2788-2799

Abstract: A well†known result of J. Lindenstrauss and A. Pełczyński (1968) gives the existence of a universal non†weakly compact operator between Banach spaces. We show the existence of universal non†Rosenthal, non†limited, and non†Grothendieck operators. We also prove that there does not exist a universal non†Dunford–Pettis operator, but there is a universal class of non†Dunford–Pettis operators. Moreover, we show that, for several classes of polynomials between Banach spaces, including the non†weakly compact polynomials, there does not exist a universal polynomial.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201600428

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:290:y:2017:i:17-18:p:2788-2799

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().