• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1823-1830
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.603-611
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.1
• /
• pp.19-28
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.113-119
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.205-209
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.319-357
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.831-836
• /
• 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, $0 \leq m \leq \infty$.

• Journal of Korean Society for Geospatial Information Science
• /
• v.17 no.3
• /
• pp.115-120
• /
• 2009

Point-based methods with experienced human operators are processed well in traditional photogrammetric activities but not the autonomous environment of digital photogrammetry. To develop more robust and accurate techniques, higher level objects of straight linear features accommodating element other than points are adopted instead of points in aerial triangulation. Even though recent advanced algorithms provide accurate and reliable linear feature extraction, extracting linear features is more difficult than extracting a discrete set of points which can consist of any form of curves. Control points which are the initial input data and break points which are end points of piecewise curves are easily obtained with manual digitizing, edge operators or interest operators. Employing high level features increase the feasibility of geometric information and provide the analytical and suitable solution for the advanced computer technology.

• Journal of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.527-538
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.601-618
• /
• 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.