• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.541-550
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• 2016

In this paper, we introduce a quasi-Banach algebra of infinite matrices, which is inverse-closed in the Banach algebra B(${\ell}^2$) of all bounded operators on ${\ell}^2$.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.575-585
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• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.29-40
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• 2010

In this paper, we study a generalization of the Banach space B($l_2$) of all bounded linear operators on $l_2$. Over this space, we present some reasonable ways to define Schatten-type classes which are generalizations of the classical Schatten classes of compact operators on $l_2$.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• East Asian mathematical journal
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• v.31 no.5
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• pp.635-652
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• 2015

It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.69-79
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• 2020

In this paper, we study the properties of T satisfying [CTC, T] = 0 for some conjugation C where [R, S] := RS - SR. In particular, we show that if T is normal, then [CTC, C] = 0. Moreover, the class of operators T satisfy [CTC, T] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T|C, |T|] = 0.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.281-286
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• 2008

In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.127-145
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• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.39-46
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• 2006

We establish a general theorem to approximate fixed points of quasicontractive operators on a normed space through the Noor iteration process with errors in the sense of Liu [9]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.889-896
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• 2021

Let 𝜙 be an entire self map on ℂ and let 𝜓 be an entire function on ℂ. A weighted composition operator induced by 𝜙 with weight 𝜓 is given by C_𝜓,𝜙. In this paper we investigate under what conditions the weighted composition operators C_𝜓,𝜙 on the Fock space over ℂ induced by 𝜙 with weight of the form $k_c({\zeta})=e^{{\langle}{\zeta},c{\rangle}-{\frac{{\mid}c{\mid}^2}{2}}}$ is normaloid and essentially normaloid.