On the Symbols of Strictly m -Null Elementary Operators

Isabel Marrero ()
Additional contact information
Isabel Marrero: Departamento de Análisis Matemático, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain

Mathematics, 2025, vol. 13, issue 12, 1-23

Abstract: This paper extends the previous work by the author on m -null pairs of operators in Hilbert space. If an elementary operator L has elementary symbols A and B that are p -null and q -null, respectively, then L is ( p + q − 1 ) -null. Here, we prove the converse under strictness conditions, modulo some nonzero multiplicative constant—if L is strictly ( p + q − 1 ) -null, then a scalar λ ≠ 0 exists such that λ A is strictly p -null and λ − 1 B is strictly q -null. Our constructive argument relies essentially on algebraic and combinatorial methods. Thus, the result obtained by Gu on m -isometries is recovered without resorting to spectral analysis. For several operator classes that generalize m -isometries and are subsumed by m -null operators, the result is new.

Keywords: elementary operator; m -isometry; m -null operators; ( m , T)-null operators; operator arithmetic progression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/12/2026/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/12/2026/ (text/html)

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:gam:jmathe:v:13:y:2025:i:12:p:2026-:d:1682934

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().