Ji Eun Lee

OPERATORS WITH THE SINGLE VALUED EXTENSION PROPERTY

In this Paper We Study some Operators With the single valued extension property. In particular, we investigate the Helton class of an operator and an triangular operator matrix T.

On the helton class of p-hyponormal operators

In this paper we show that the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has its interior in the plane.

INHERITED PROPERTIES THROUGH THE HELTON CLASS OF AN OPERATOR

In this paper we show that Helton class preserves the nilpotent and finite ascent properties. Also, we show some relations on non-transitivity and decomposability between operators and their Helton classes. Finally, we give some applications in the Helton class of weighted shifts.

Normal truncated Toeplitz operators on finite-dimensional spaces

In this paper, we characterize normal matrices on finite-dimensional spaces. Moreover, we provide some conditions for truncated Toeplitz operators (defined below) on finite-dimensional spaces to be normal and give several examples of such operators. Finally, we study symbols of normal truncated Toeplitz operators on finite-dimensional spaces.

SKEW COMPLEX SYMMETRIC OPERATORS AND WEYL TYPE THEOREMS

An operator T 2 L(H) is said to be skew complex symmetric if there exists a conjugation C on H such that T = CT ∗ C. In this pa- per, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we con- sider Weyl type theorems and Browder type theorems for skew complex symmetric operators. Let L(H) be the algebra of all bounded linear operators on a separable complex Hilbert space H and let K(H) be the ideal of all compact operators on H. If T ∈ L(H), we write �(T), �(T), �su(T), �comp(T), �r(T), �c(T), �a(T), �e(T), �le(T), andre(T) for the resolvent set, for the spectrum, the surjective spectrum, the compression spectrum, the residual spectrum, the continuous spectrum, the approximate point spectrum, the essential spectrum, the left essential spectrum, and the right essential spectrum of T, respectively. A conjugation on H is an antilinear operator C : H → H which satisfies hCx,Cyi = hy,xi for all x,y ∈ H and C 2 = I. An antiunitary operator is

SOME REMARKS ON THE HELTON CLASS OF AN OPERATOR

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunfords boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponor- mal operators or decomposable subnormal operators satisfles Dunfords boundedness condition (B).

Remark on complex symmetric operator matrices

In this paper, we study conjugation matrices and complex symmetric operator matrices. In particular, we investigate conditions for operator matrices to be conjugations or complex symmetric on . Using these results, we provide examples of conjugation matrices and complex symmetric operators. Finally, we apply the main results to block Toeplitz operators and completion problems.

A characterization of binormal matrices

Abstract We give a characterization of binormal operator matrices, and in particular, a description of binormal Toeplitz matrices for . Non-trivial examples of binormal matrices that are not normal are also provided.

On n-quasi-(m,C)-isometric operators

ABSTRACT In this paper, we introduce the class of n-quasi- -isometric operator on a Hilbert space which is a variation of -isometric operators Chō M, Ko E, Lee JE. [On -isometric operators. Complex Anal Oper Theory. 2016;10:1679–1694]. An operator is said to be n-quasi- -isometric if for some positive integers n and m. We study this class of such operators and give some of their basic properties.

On rank one perturbations of the unilateral shift

In this paper we study some properties of rank one perturba- tions of the unilateral shift operators T = S+u v. In particular, we give some criteria for eigenvalues of T. Also we characterize some conditions for T to be hyponormal.