• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.937-958
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• 1996

On the setting of product of balls we consider Toeplitz operators, with symbols satisfying a certain condition, on the Bergman space. Norms and essential norms of such operators are estimated by means of certain integral quantities.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.15-25
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• 2016

We obtain some estimations of the essential norm of a pull back operator induced by quasi-symmetric homeomorphisms. As a corollary, we deduce the compactness criterion of this operator.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.137-159
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• 2013

It is studied the linear combinations of composition operators on the Banach space of bounded harmonic functions on the open unit disk. We determine the essential norm of them.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.619-629
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• 2019

On the setting of the pluriharmonic Dirichlet space, we describe the essential norm of an operator which is a finite sum of products of several Toeplitz operators.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.651-669
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• 2021

In this paper, we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball 𝔹. We also characterize the boundedness, compactness and find the essential norm estimates for composition operators between these spaces.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.583-591
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• 2003

For a weighted composition operator $uC_{\varphi}$ on C(X), we determine its essential norm and the constant for its Hyers-Ulam stability, in terms of the set $\varphi(\{x\;\in\;X\;:\;$\mid$u(x)$\mid$\;\geq\;r\})$ (r > 0).

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1711-1719
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• 2015

We obtain a new criterion for the boundedness and compactness of the weighted composition operators ${\psi}C_{\varphi}$ from ${\ss}^{{\alpha}}$(0 < ${\alpha}$ < 1) to ${\ss}^{{\beta}}$ in terms of the sequence $\{{\psi}{\varphi}^n\}$. An estimate for the essential norm of ${\psi}C_{\varphi}$ is also given.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.533-541
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• 2006

let E be a Finsler modules over $C^*$-algebras. A with norm-map $\rho$ and L(E) set of all A-linear bonded operators on E. We show that the canonical homomorphism ${\phi}:L(E){\rightarrow}L(E_I)$ sending each operator T to its restriction $T|E_I$ is injective if and only if I is an essential ideal in the underlying $C^*$-algebra A. We also show that $T{\in}L(E)$ is a bounded below if and only if ${\mid}{\mid}x{\mid}{\mid}={\mid}{\mid}{\rho}{\prime}(x){\mid}{\mid}$ is complete, where ${\rho}{\prime}(x)={\rho}(Tx)$ for all $x{\in}E$. Also, we give a necessary and sufficient condition for the equivalence of the norms generated by the norm map.