Eungil Ko
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View article: Binormal block Toeplitz operators with matrix valued circulant symbols
Binormal block Toeplitz operators with matrix valued circulant symbols Open
This paper focuses on the binormality of block Toeplitz operators with matrix valued circulant symbols. We also study some Γ-dilations of Toeplitz operators. Moreover, we also analyze the invariant subspace of Toeplitz operators with matri…
View article: Hyponormality of Toeplitz operators on Newton spaces
Hyponormality of Toeplitz operators on Newton spaces Open
In this paper, we investigate properties of hyponormal Toeplitz operators whose symbols are analytic or co-analytic on a Newton space. We establish both necessary and sufficient conditions for a Toeplitz operator $$T_{\varphi }$$ to be…
View article: The operator equation AXB=X and the Fuglede-Putnam type property
The operator equation AXB=X and the Fuglede-Putnam type property Open
In this paper, we study some connections between solutions A and B satisfying the operator equation AXB = X .We also investigate several properties between such solutions A and B .In particular, we show that if A has the single valued exte…
View article: Hankel and Toeplitz operators, block matrices and derivations
Hankel and Toeplitz operators, block matrices and derivations Open
Hankel and Toeplitz operators are the compressions of Laurent and bilateral Hankel operators, which in turn can be presented as two-by-two operator matrices with Toeplitz and Hankel entries.
View article: Remark on the dilation of truncated Toeplitz operators
Remark on the dilation of truncated Toeplitz operators Open
An operator Su ?,? on L2 is called the dilation of a truncated Toeplitz operator if for two symbols ?,? ? L? and an inner function u, Su ?,? f = ?Pu f + ?Qu f holds for f ? L2 where Pu is the orthogonal projection of L2 onto K2 u and Qu = …
View article: Remarks on n-power quasinormal operators
Remarks on n-power quasinormal operators Open
In this paper, we study properties and structures of n-power quasinormal operators. In particular, we show that every n-power quasinormal operator satisfies some local spectral properties. Finally, we consider the n-power quasinormality of…
View article: Complex symmetric Toeplitz operators on the generalized derivative Hardy space
Complex symmetric Toeplitz operators on the generalized derivative Hardy space Open
The generalized derivative Hardy space $S^{2}_{\alpha ,\beta}(\mathbb{D})$ consists of all functions whose derivatives are in the Hardy and Bergman spaces as follows: for positive integers α , β , $$ S^{2}_{\alpha ,\beta}(\mathb…
View article: On hyponormality of the sum of two composition operators
On hyponormality of the sum of two composition operators Open
In this paper we study some properties of the sums of two composition operators on the Hardy space. In particular, we investigate hyponormality of the sums of two composition operators. We also provide some conditions for which the sums of…
View article: On backward Aluthge iterates of complex symmetric operators
On backward Aluthge iterates of complex symmetric operators Open
For a nonnegative integer k , an operator T ∈ L (H ) is called a backward Aluthge iterate of a complex symmetric operator of order k if the k th Aluthge iterate T (k) of T is a complex symmetric operator, denoted by T ∈ BAIC(k) .In this pa…
View article: On quasinormality of the dilation of truncated Toeplitz operators
On quasinormality of the dilation of truncated Toeplitz operators Open
An operator S u ϕ,ψ on L 2 is called the dilation of a truncated Toeplitz operator if for two symbols ϕ,ψ ∈ L ∞ and an inner function u , S u ϕ,ψ
View article: On extended commuting operators
On extended commuting operators Open
In this paper, we study properties of extended commuting operators. In particular, we provide the polar decomposition of the product of (?,?)-commuting operators where ? and ? are real numbers with ?? > 0. Furthermore, we find the restrict…
View article: Operator matrices and their Weyl type theorems
Operator matrices and their Weyl type theorems Open
We denote the collection of the 2 x 2 operator matrices with (1,2)-entries having closed range by S. In this paper, we study the relations between the operator matrices in the class S and their component operators in terms of the Drazin sp…
View article: On the iterated mean transforms of operators
On the iterated mean transforms of operators Open
Let T = U|T | be the polar decomposition of an operator T ∈ L (H ) .For given s,t 0 , we say that T s,t := sU|T | + t|T |U is the weighted mean transform of T .In this paper, we study properties of the k -th iterated weighted mean transfor…
View article: n-fold Jordan product commuting maps with a λ-Aluthge transform
n-fold Jordan product commuting maps with a λ-Aluthge transform Open
Let B(H) be the set of all bounded linear operators from H to H , where H is a complex Hilbert space.In this paper, we study the properties of T when the λ -Aluthge transform of T n is T .Also we prove that the bijective map Φ : B(H) → B(K…
View article: m-Isometric block Toeplitz operators
m-Isometric block Toeplitz operators Open
In this paper, we study m-isometric block Toeplitz operators with trigonometric symbols. In addition, we give a necessary and sufficient condition for block Toeplitz operators with trigonometric polynomial symbols to be m-contractive.
View article: Remark on skew $m$-complex symmetric operators (Research on structure of operators using operator means and related topics)
Remark on skew $m$-complex symmetric operators (Research on structure of operators using operator means and related topics) Open
In this paper we study skew m-complex symmetric operators. In particular, we prove that if Tin mathcal{L}(mathcal{H}) is a skew m-complex symmetric operator with a conjugation C, then e^{itT}, e^{-itT}, and e^{-itT^{*}} are (m, C)-isometri…
View article: On complex symmetric block Toeplitz operators
On complex symmetric block Toeplitz operators Open
In this paper, we study complex symmetry of Toeplitz operators and block Toeplitz operators. In particular, we give a characterization of complex symmetric block Toeplitz operators with the special conjugation on the vector-valued Hardy sp…
View article: On power similarity of complex symmetric operators
On power similarity of complex symmetric operators Open
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…
View article: Skew m-complex symmetric operators
Skew m-complex symmetric operators Open
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, w…
View article: Local spectral property of 2 x 2 operator matrices
Local spectral property of 2 x 2 operator matrices Open
In this paper we study the local spectral properties of 2 x 2 operator matrices. In particular, we show that every 2 x 2 operator matrix with three scalar entries has the single valued extension property. Moreover, we consider the spectral…
View article: Remarks on nearly equivalent operators
Remarks on nearly equivalent operators Open
An operator S ∈ L (H ) is said to be nearly equivalent to T if there exists an invertible operator V ∈ L (H ) such that S * S = V -1 T * TV .In this paper, we study several properties of nearly equivalent
View article: On properties of the operator equation TT*=T+T*
On properties of the operator equation TT*=T+T* Open
In this paper, we study properties of the operator equation TT*=T+T* which T.T. West observed in [12]. We first investigate the structure of solutions T 2 B(H) of such equation. Moreover, we prove that if T is a polynomial root of solution…
View article: On symmetric and skew-symmetric operators
On symmetric and skew-symmetric operators Open
In this paper we show many spectral properties that are inherited by m-complex symmetric and m-skew complex symmetric operators and give new results or recapture some known ones for complex symmetric operators.
View article: Almost invariant half-spaces for operators on Hilbert space. II:\n operator matrices
Almost invariant half-spaces for operators on Hilbert space. II:\n operator matrices Open
This paper is a sequel to [6]. In that paper we transferred the discussions\nin [1] and [13] concerning almost invariant half-spaces for operators on\ncomplex Banach spaces to the context of operators on Hilbert space, and we gave\neasier …
View article: Almost invariant half-spaces for operators on Hilbert space. II: operator matrices
Almost invariant half-spaces for operators on Hilbert space. II: operator matrices Open
This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier pro…
View article: ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE
ALMOST INVARIANT HALF-SPACES FOR OPERATORS ON HILBERT SPACE Open
The theory of almost invariant half-spaces for operators on Banach spaces was begun recently and is now under active development. Much less attention has been given to almost invariant half-spaces for operators on Hilbert space, where some…
View article: On a conjugation and a linear operator (The research of geometric structures in quantum information based on Operator Theory and related topics)
On a conjugation and a linear operator (The research of geometric structures in quantum information based on Operator Theory and related topics) Open
In this note, we introduce the study of some classes of operators concerning with conjugations on a complex Hilbert space.