Year: 2025
Type: article
Abstract: An unbounded product $$T=AB$$ T = A B of two nonnegative selfadjoint operators A and B , where $$\rho (T) \ne \emptyset $$ ρ ( T ) ≠ ∅ and A is bounded, is proved to have the single valued extension property (SVEP) and, more significantly, to be a $$\mathbb {C}$$ C -generalized scalar operator. This property plays a central role as, it not only implies the Dunford’s property for the product AB , but it also allows any operator T that is quasi-affine to a nonnegative selfadjoint operator S to satisfy $$\sigma (T)=\sigma (S)$$ σ ( T ) = σ ( S ) . These results have required a deeper study of the spectral connection between operators S having SVEP and Dunford properties and operators T that are quasi-affine to S .
Authors: Yosra Barkaoui, Seppo Hassi
Institution: University of Vaasa
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Vaasan yliopisto
OpenAlex ID: W4414927771