• 대한수학회지
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• 제50권6호
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• 대한수학회보
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• 제54권3호
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• pp.747-761
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• 2017

We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.

• 충청수학회지
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• 제22권4호
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• pp.727-737
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• 2009

Let M(X) be the space of all pointwise multipliers of Banach space X. We will show that, for each $\alpha>1$, $M(\mathfrak{B}_\alpha)=M(\mathfrak{B}_{\alpha,0})=H^\infty{(B)}$. We will also show that, for each $0<{\alpha}<1$, $M(\mathfrak{B}_\alpha)$ and $M(\mathfrak{B}_{\alpha,0})$ are Banach algebras. It is established that certain inclusion relationships exist between the weighted Bloch spaces and holomorphic Besov spaces.

• 대한수학회보
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• 제47권2호
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• pp.369-383
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• 2010

We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• 대한수학회지
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• 제45권5호
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• pp.1203-1220
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• 2008

Let V be an arbitrary system of weights on an open connected subset G of ${\mathbb{C}}^N(N{\geq}1)$ and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let $HV_b$ (G, E) and $HV_0$ (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings ${\phi}:G{\rightarrow}G$ and operator-valued analytic mappings ${\Psi}:G{\rightarrow}B(E)$ which generate weighted composition operators and invertible weighted composition operators on the spaces $HV_b$ (G, E) and $HV_0$ (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights.

• 대한수학회지
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• 제32권4호
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• pp.679-688
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• 1995

Let $(B, \left\$\mid$ \right\$\mid$)$ be a real separable Banach space. Let $(\Omega, F, P)$ denote a probability space. A random elements in B is a function from $\Omega$ into B which is $F$-measurable with respect to the Borel $\sigma$-field $B$(B) in B.

• 충청수학회지
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• 제23권3호
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• pp.523-534
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• 2010

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

• 대한수학회논문집
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• 제35권4호
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• pp.1159-1170
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• 2020

We consider the weighted spaces ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓) for 1 < p < +∞, where 𝜑 and 𝜓 are weights on 𝕊 (= ℕ or ℤ). We obtain a sufficient condition for ℓ^p(𝕊, 𝜓) to be multiplier weighted-space of ℓ^p(𝕊, 𝜑) and ℓ^p(𝕊, 𝜓). Our condition characterizes the last multiplier weighted-space in the case where 𝕊 = ℤ. As a consequence, in the particular case where 𝜓 = 𝜑, the weighted space ℓ^p(ℤ,𝜓) is a convolutive algebra.

• 대한수학회지
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• 제35권1호
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• pp.177-189
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• 1998

In this paper, weighted Bloch spaces $B_q (q > 0)$ are considered on the open unit ball in $C^n$. These spaces extend the notion of Bloch spaces to wider classes of holomorphic functions. It is proved that the functions in a weighted Bloch space admit certain integral representation. This representation formula is then used to determine the degree of growth of the functions in the space $B_q$. It is also proved that weighted Bloch space is a Banach space for each weight q > 0, and the little Bloch space $B_q,0$ associated with $B_q$ is a separable subspace of $B_q$ which is the closure of the polynomials for each $q \geq 1$.