Perturbation of the spectra of complex symmetric operators

An operator T on a complex Hilbert space H is called complex symmetric if T has a symmetric matrix representation relative to some orthonormal basis for H. This paper focuses on the perturbation theory for the spectra of complex symmetric operators. We prove that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and having the single-valued extension property. Also it is proved that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and satisfying generalized Weyl?s theorem.

On power similarity of complex symmetric operators

In this paper, we study properties of operators which are power similar to complex symmetric operators. In particular, we prove that if T is power similar to a complex symmetric operator, then T is decomposable modulo a closed set S ? C if and only if R has the Bishop?s property (?) modulo S. Using the results, we get some applications of such operators.

Skew m-complex symmetric operators

In this paper we study skew m-complex symmetric operators. In particular, we show that if T ? L(H) is a skew m-complex symmetric operator with a conjugation C, then eitT , e-itT , and e-itT* are (m,C)-isometric for every t ? R. Moreover, we examine some conditions for skew m-complex symmetric operators to be skew (m-1)-complex symmetric.

ON ∞-COMPLEX SYMMETRIC OPERATORS

In this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property (δ) if and only if T is decomposable. Moreover, we show that if T and S are ∞-complex symmetric operators, then so is T ⊗ S.

Weyl type theorems for complex symmetric operator matrices

In this paper, we study Weyl type theorems for complex symmetric operator matrices. In particular, we give a necessary and sufficient condition for complex symmetric operator matrices to satisfy a-Weyl?s theorem. Moreover, we also provide the conditions for such operator matrices to satisfy generalized a-Weyl?s theorem and generalized a-Browder?s theorem, respectively. As some applications, we give various examples of such operator matrices which satisfy Weyl type theorems.