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A Remark on Support of the Principal Function for Class A Operators
Authors:Muneo Chō  Mariko Giga  Tadasi Huruya  Takeaki Yamazaki
Affiliation:(1) Department of Mathematics, Kanagawa University, Yokohama 221-8686, Japan;(2) Department of Mathematics, Nippon Medical School, Kawasaki 221-0063, Japan;(3) Faculty of Education and Human Sciences, Niigata University, Niigata 950-2181, Japan
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 
$$ {text{supp(gT)}} = sigma {text{(T)}} $$
.
Keywords:  KeywordHeading"  >Mathematics Subject Classification (2000). Primary 47B20  Secondary 47A10
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