• Bulletin of the Korean Mathematical Society
• /
• 제53권6호
• /
• 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
• /
• 제43권2호
• /
• pp.389-393
• /
• 2006

In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

• Bulletin of the Korean Mathematical Society
• /
• 제40권4호
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• 제26권3호
• /
• pp.467-475
• /
• 2013

We consider the problem to determine when a Toeplitz operator is bounded on weighted Bergman spaces. We introduce some set CG of symbols and we prove that Toeplitz operators induced by elements of CG are bounded and characterize when Toeplitz operators are compact and show that each element of CG is related with a Carleson measure.

• Journal of the Korean Mathematical Society
• /
• 제57권2호
• /
• pp.429-450
• /
• 2020

We prove that wave operators for Schrödinger operators with multi-center local point interactions are scaling limits of the ones for Schrödinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.

• Bulletin of the Korean Mathematical Society
• /
• 제34권1호
• /
• 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.

• East Asian mathematical journal
• /
• 제21권2호
• /
• pp.191-203
• /
• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• Journal of the Chungcheong Mathematical Society
• /
• 제24권1호
• /
• 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
• /
• 제56권3호
• /
• pp.585-596
• /
• 2019

It is shown that a pair of Hilbert space operators V and W such that $V^*W=I$ (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal bases are replaced with biorthogonal sequences, and it is also shown how such a pair of biisometric operators yields a pair of biorthogonal sequences which are shifted by them. These are applied to a class of Laguerre operators on $L^2[0,{\infty})$.

• Journal of the Korean Mathematical Society
• /
• 제6권2호
• /
• pp.55-73
• /
• 1969