Disjoint p$p$‐convergent operators and their adjoints

Geraldo Botelho, Luis Alberto Garcia and Vinícius C. C. Miranda

Mathematische Nachrichten, 2024, vol. 297, issue 12, 4766-4777

Abstract: First, we give conditions on a Banach lattice E$E$ so that an operator T$T$ from E$E$ to any Banach space is disjoint p$p$‐convergent if and only if T$T$ is almost Dunford–Pettis. Then, we study when adjoints of positive operators between Banach lattices are disjoint p$p$‐convergent. For instance, we prove that the following conditions are equivalent for all Banach lattices E$E$ and F$F$: (i) a positive operator T:E→F$T: E \rightarrow F$ is almost weak p$p$‐convergent if and only if T∗$T^*$ is disjoint p$p$‐convergent; (ii) E∗$E^*$ has order continuous norm or F∗$F^*$ has the positive Schur property of order p$p$. Very recent results are improved, examples are given and applications of the main results are provided.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202300561

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:297:y:2024:i:12:p:4766-4777

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 ().