Back to Search
Start Over
A C*-ALGEBRA APPROACH TO COMPLEX SYMMETRIC OPERATORS.
- Source :
-
Transactions of the American Mathematical Society . Oct2015, Vol. 367 Issue 10, p6903-6942. 40p. - Publication Year :
- 2015
-
Abstract
- In this paper, certain connections between complex symmetric operators and anti-automorphisms of singly generated C*-algebras are established. This provides a C*-algebra approach to the norm closure problem for complex symmetric operators. For T ∈ B(H) satisfying C*(T)∩K(H) = {0}, we give several characterizations for T to be a norm limit of complex symmetric operators. As applications, we give concrete characterizations for weighted shifts with nonzero weights to be norm limits of complex symmetric operators. In particular, we prove a conjecture of Garcia and Poore. On the other hand, it is proved that an essentially normal operator is a norm limit of complex symmetric operators if and only if it is complex symmetric. We obtain a canonical decomposition for essentially normal operators which are complex symmetric. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 367
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 108872404