Showing papers by "Muneo Chō published in 2007"
TL;DR: In this paper, it was shown that if T is pure, then if gT is the principal function of T, then GT is a class A operator such that gT subseteq \sigma σ(T) σ + σ σ (T) = σσσ(T), where σ is the ratio of gT to T.
Abstract: Let
$$ T = U{\left| T \right|} $$
be an invertible class A operator such that
$$ [T^{{*\,}} ,T] \in C_{1} $$
. Then we show that
$$ {\text{supp(gT)}} \subseteq \sigma {\text{(T)}} $$
, where gT is the principal function of T. Moreover, we show that if T is pure, then
$$ {\text{supp(gT)}} = \sigma {\text{(T)}} $$
.
9 citations