• 대한수학회보
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• 제53권6호
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• pp.1823-1830
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• 2016

Let H and K be two Hilbert spaces, and let A and B be two bounded linear operators from H to K. We are interested in $RangeB^*{\supseteq}RangeA^*$. It is well known that this is equivalent to the inequality $A^*A{\geq}{\varepsilon}B^*B$ for a positive constant ${\varepsilon}$. We study conditions in terms of symbols when A and B are singular integral operators, Hankel operators or Toeplitz operators, etc.

• 대한수학회보
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• 제40권4호
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• pp.603-611
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• 2003

In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.

• 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.

• 충청수학회지
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• 제24권1호
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• pp.113-119
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• 2011

Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

• 대한수학회보
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• 제32권2호
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• pp.205-209
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• 1995

Throughout this paper X is a Banach space and $\mu$ is the Lebesgue measure on [0, 1] and all operators are assumed to be bounded and linear. $L^1(\mu)$ is the Banach space of all (classes of) Lebesgue integrable functions on [0, 1] with its usual norm. Let $T : L^1(\mu) \to X$ be an operator.

• 대한수학회지
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• 제54권1호
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• 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, $0 \leq m \leq \infty$.

• 대한공간정보학회지
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• 제17권3호
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• pp.115-120
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• 2009

기존의 도화사 수작업에 의한 기준점기반 항공삼각측량 기법은 전통적인 사진측량에서 유용하게 이용되어 왔으나, 자동화된 수치사진측량 기법이 확산되면서 기존방법의 문제점이 대두되었다. 따라서 본 논문은 보다 발전된 자동화 기술 개발을 위하여 상위 레벨인 선형객체들을 이용한 항공삼각측량 가능성을 제시하고 검증하고자 하였다. 최근에 발달된 선형 객체 추출기법 알고리즘은 보다 정확한 선형 객체 추출기법을 제공하였지만, 포인트 추출기법에 비하여 추출하기 어려운 단점이 존재한다. 따라서 본 논문은 이를 극복하기 위하여 수동 디지타이징이나 에지 연산자를 통하여 쉽게 획득되는 포인트를 이용하여 상위레벨 선형객체를 생성하고, 이를 통해 지형공간정보 이용 가능성을 높이고자 하였다. 본 연구 결과를 통해 진화하고 있는 컴퓨터 환경에 적합한 선형객체를 이용한 항공삼각측량 기법을 발전시킬 것으로 기대된다.

• 대한수학회지
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• 제35권3호
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• pp.527-538
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• 1998

We study on kernel operators (Wick monomials) on symmetric Fock space. We give optimal conditions on kernels so that the corresponding kernel operators are densely defined linear operators on the Fock space. We try to formulate our results in the framework of white noise analysis as much as possible. The most of the results in this paper can be extended to anti-symmetric Fock space.

• 대한수학회보
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• 제37권3호
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• pp.601-618
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• 2000

Let (and $g^*$) be the space of regular test (and generalized, resp.) white noise functions. The integral kernel operators acting on and transformation groups of operators on are studied, and then every integral kernel operator acting on can be extended to continuous linear operator on $g^*$. The existence and uniqueness of solutions of Cauchy problems associated with certain integral kernel operators with intial data in $g^*$ are investigated.