caa a22 4500 469043210 CHVBK 20180323132816.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF01193771 doi (NATIONALLICENCE)springer-10.1007/BF01193771 Xia Daoxing Department of Mathematics, Vanderbilt University, 37235, Nashville, TN, USA aut Complete unitary invariant for some subnormal operator [Elektronische Daten] [Daoxing Xia] IfS is a subnormal operator with minimal normal extensionN satisfying the conditions that (i) $$\left[ {S^* ,S} \right]^{\frac{1}{2}} \in \mathcal{L}^1$$ , (ii) sp (S) is the unit disk and (iii) sp (N)={N: |z|=1 orz=a 1,...,a k then $$tr\left( {\left[ {S^* ,(\lambda I - S)^{ - 1} } \right]\left[ {S^* ,(\mu I - S)^{ - 1} } \right]} \right) = \frac{n}{{\lambda ^2 \mu ^2 }} + \sum\limits_{i,j = 1}^k {\frac{{\gamma ij}}{{\lambda \mu (\lambda - a_i )(\mu - a_j )}}} $$ . wheren=index ( $$S^* - \bar zI$$ ) forz∈sp (S)/sp (N) and (γij) is a real symmetric matrix. The set {n, γij,i,j = 1,...,k} is a complete unitary invariant for an operator in the class of all irreducible subnormal operators satisfying conditions (i), (ii), (iii) and that there is at least one positive simple eigenvalue of [S *,S]. Birkhäuser Verlag, 1992 Integral Equations and Operator Theory Birkhäuser-Verlag 15/1(1992-01-01), 154-166 0378-620X 15:1<154 1992 15 20 https://doi.org/10.1007/BF01193771 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01193771 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Xia Daoxing Department of Mathematics, Vanderbilt University, 37235, Nashville, TN, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/1(1992-01-01), 154-166 0378-620X 15:1<154 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer