• 대한수학회논문집
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• 제35권2호
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• pp.547-563
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• 2020

We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown.

• Korean Journal of Mathematics
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• 제25권2호
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• pp.247-259
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• 2017

By the use of inequalities for nonnegative Hermitian forms some new inequalities for numerical radius of bounded linear operators in complex Hilbert spaces are established.

• 호남수학학술지
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• 제43권3호
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• pp.523-537
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• 2021

In this paper, we obtain some new inequalities for the Berezin number of operators on reproducing kernel Hilbert spaces by using the Hölder-McCarthy operator inequality. Also, we give refine generalized inequalities involving powers of the Berezin number for sums and products of operators on the reproducing kernel Hilbert spaces.

• 충청수학회지
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• 제35권3호
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• pp.269-275
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• 2022

In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.

• 대한수학회지
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• 제53권2호
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• pp.347-362
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• 2016

In this paper, we are concerned with abstract random linear operators on probabilistic unitary spaces which are a generalization of generalized random linear operators on a Hilbert space defined in [25]. The representation theorem for abstract random bounded linear operators and some results on the adjoint of abstract random linear operators are given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권2호
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• pp.137-149
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• 2006

We introduce the notion of the generalized covariance and variance for bounded linear operators on Hilbert space, and prove that the generalized covariance-variance inequality holds. It turns out that the inequality is a useful formula in tile study of inequality involving linear operators in Hilbert spaces.

• 대한수학회보
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• 제60권1호
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• pp.123-135
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• 2023

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of α-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.

• 대한수학회지
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• 제38권1호
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• pp.177-191
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• 2001

We consider a linear differential game described by the delay-differential equation in a Hilbert space H; (※Equations, See Full-text) U and V are Hilbert spaces, and B(t) and C(t) are families of bounded operators on U and V to H, respectively. A(sub)0 generates an analytic semigroup T(t) = e(sup)tA(sub)0 in H. The control variables g, and u and v are supposed to be restricted in the norm bounded sets (※Equations, See Full-text). For given x(sup)0 ∈ H and a given time t > 0, we study $\xi$-approximate controllability to determine x($.$) for a given g and v($.$) such that the corresponding solution x(t) satisfies ∥x(t) - x(sup)0∥ $\leq$ $\xi$($\xi$ > 0 : a given error).

• 대한수학회보
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• 제34권1호
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• 대한수학회논문집
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• 제9권4호
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• pp.831-836
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• 1994

In this paper we characterize the quasiaffine transforms of quasisubscalar operators. Let H and K be separable, complex Hilbert spaces and L(H,K) denote the space of all linear, bounded operators from H to K. If H = K, we write L(H) in place of L(H,K). A linear bounded operators S on H is called scalar of order m if there is a continuous unital morphism of topological algebras $$ \Phi : C^m_0(C) \to L(H) $$ such that $\Phi(z) = S$, where as usual z stands for identity function on C, and $C^m_0(C)$ stands for the space of compactly supproted functions on C, continuously differentiable of order m, $0 \leq m \leq \infty$.