An operator T ∈L(H) is said to be complex symmetric if there exists a conjugation C on H such that T =CT∗C. In this paper, we prove that every complex symmetric operator is biquasitriangular. Also, we show that if a complex symmetric operator T is weakly hypercyclic, then both T and T∗ have the single-valued extension property and that if T is a complex symmetric operator which has the property (δ), then Weyl’s theorem holds for f (T) and f (T)∗ where f is any analytic function in a neighborhood of σ (T). Finally, we establish equivalence relations among Weyl type theorems for complex symmetric operators.
|Number of pages||2|
|Journal||Operators and Matrices|
|State||Published - 1 Dec 2014|
- Complex symmetric operator
- Weakly hypercyclic
- Weyl type theorem