On the Symbols of Strictly m-Null Elementary Operators
Year: 2025
Type: article
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 λA is strictly p-null and λ−1B 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.
Source: Mathematics
DOI: 10.3390/math13122026
Author: Isabel Marrero
Institution: Universidad de La Laguna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4411451588