• Korean Journal of Mathematics
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• v.7 no.2
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• pp.207-213
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• 1999

In this paper we estimate a lower bound of the Banach-Mazur distance between a finite dimensional nonlocally convex space and its Banach envelope space by investigating the properties of the nonlocally convex space and the projection constant which are obtained by factoring the identity operator through $l^k_{\infty}$ on the quasi-normed spaces.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.793-806
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• 2016

G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and ${\beta}$-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results regarding the existence of g-vector-valued sequence space frames and g-Banach frames are obtained. In particular, it is proved that if X is a separable Banach space and Y is a Banach space with a Schauder basis, then there exist a Y-valued sequence space $Y_v$ and a g-Banach frame for X with respect to Y and $Y_v$.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.427-430
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• 2009

In this paper we introduce the intermediate differential of a Lipschitz map from a Banach space to another Banach space and prove that every locally Lipschitz function f defined on an open subset ${\Omega}$ of a superreflexive real Banach space X to a finite dimensional Banach space Y is uniformly intermediate differentiable at every point ${\Omega}/A$, where A is a ${\sigma}$-lower porous set.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.137-140
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• 2009

In this paper, we introduce and formulate the definitions of Banach operator type k and Banach operator pair on intuitionistic fuzzy metric space. Thereafter we prove some properties and theorems on intuitionistic fuzzy metric space.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.347-354
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• 2008

In this paper, we will show that ($CF(X,K),{\chi}_{{\parallel}{\mid}{\cdot}{\parallel}{\mid}}$) is a fuzzy Banach space using that the dual space $X^*$ of a normed linear space X is a crisp Banach space. And for a normed linear space Y instead of a scalar field K, we obtain ($CF(X,Y),{\rho}^*$) is a fuzzy Banach space under the some conditions.

• East Asian mathematical journal
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• v.24 no.1
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• pp.57-65
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• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1387-1401
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• 2019

Consider a finite measure space (${\Omega}$, ${\Sigma}$, ${\mu}$) and a Banach space $X({\mu})$ consisting of (equivalence classes of) real measurable functions defined on ${\Omega}$ such that $f{\chi}_A{\in}X({\mu})$ and ${\parallel}f{\chi}_A{\parallel}{\leq}{\parallel}f{\parallel}$, ${\forall}f{\in}({\mu})$, $A{\in}{\Sigma}$. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.19-26
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• 2024

In this paper, we investigate the properties related to algebraic spectral subspaces and divisible subspaces of linear operators on a Banach space. In addition, using the concept of topological divisior of zero of a Banach algebra, we prove that the only closed divisible subspace of a bounded linear operator on a Banach space is trivial. We also give an example of a bounded linear operator on a Banach space with non-trivial divisible subspaces.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.341-348
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• 1998

In this paper, we show that Schlumprecht space is reflexive and the Dual of Schlumprecht space has the Banach-Saks property and study behavior of block basic sequence in Schlumprecht space.