An extreme example concerning factorization products on the Schwartz space 
Abstract
We construct linear operators S, T mapping the Schwartz space 𝕾 into its dual 
, such that any operator 
may be obtained as factorization product 
. More precisely, given , there exists a Hilbert space 
such that 
, the embeddings 
and 
are continuous, 
is dense in 
, 
, and S has a continuous extension 
such that 
for all φ ∈ 𝕾.
, such that any operator may be obtained as factorization product . More precisely, given , there exists a Hilbert space such that , the embeddings and are continuous, is dense in , , and S has a continuous extension such that for all φ ∈ 𝕾.DOI Code:
10.1285/i15900932v25n2p31
Keywords:
Factorization product; Partial algebra
Classification:
47L60; 47A70; 46F99; 47C99
Full Text: PDF
