• Bulletin of the Korean Mathematical Society
• /
• v.20 no.2
• /
• pp.87-93
• /
• 1983

Let X and Y be normed linear spaces. An operator T defined on X with the range in Y is continuous in the sense that if a sequence {x$_{n}$} in X converges to x for the weak topology .sigma.(X.X') then {Tx$_{n}$} converges to Tx for the norm topology in Y. We shall denote the class of such operators by WC(X, Y). For example, if T is a compact operator then T.mem.WC(X, Y). In this note we discuss relationships between WC(X, Y) and the class of weakly of bounded linear operators B(X, Y). In the last section, we will consider some characters for an operator in WC(X, Y).).

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1427-1449
• /
• 2020

In this paper, we establish the boundedness of the m-linear Calderón-Zygmund operators on product of central Morrey spaces with variable exponent. The corresponding boundedness properties of their commutators with λ-central BMO symbols are also considered. Finally, we prove that the multilinear commutators of Calderón-Zygmund singular integrals introduced by Pérez and Trujillo-Gonález are bounded on central Morrey spaces with variable exponent. Our results improve and generalize some previous classical results to the variable exponent setting.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.13-22
• /
• 2019

We compute the second cohomology of the affine Lie algebra aff(1) on the dimensional real space with coefficients in the space ${\mathcal{D}}^n_{{\underline{\lambda}},{\mu}}$ of n-ary linear differential operators acting on weighted densities where ${\underline{\lambda}}=({\lambda}_1,{\ldots},{\lambda}_n)$. We explicitly give 2-cocycles spanning these cohomology.

• Journal of applied mathematics & informatics
• /
• v.41 no.5
• /
• pp.1103-1114
• /
• 2023

The aim of the present paper is to obtain some mapping properties of subordinations by certain univalent functions in the open unit disk associated with a family of linear operators. Moreover, we also consider some applications for integral operators.

• The Pure and Applied Mathematics
• /
• v.13 no.2 s.32
• /
• pp.137-149
• /
• 2006

We introduce the notion of the generalized covariance and variance for bounded linear operators on Hilbert space, and prove that the generalized covariance-variance inequality holds. It turns out that the inequality is a useful formula in tile study of inequality involving linear operators in Hilbert spaces.

• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1181-1190
• /
• 1999

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterized the linear operators that preserve zero-term rank of the m×n matrices over binary Boolean algebra.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.715-720
• /
• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.57-65
• /
• 2009

In the papers [5]-[7] was examined approximation of functions by the modified Sz$\'{a}$sz-Mrakyan operators and other positive linear operators preserving $e_2(x)=x^2$. In this paper we introduce the Post-Widder and Stancu operators preserving $x^2$ in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.617-627
• /
• 1994

Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.457-464
• /
• 2004

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).