• 대한수학회보
• /
• 제52권2호
• /
• pp.505-511
• /
• 2015

In this paper, we investigate relationships among property ($k-{\beta}$), weak property (${\beta}_k$), k-nearly uniformly convexity and property ($A_k$).

• Korean Journal of Mathematics
• /
• 제20권4호
• /
• pp.415-422
• /
• 2012

In this paper, we define the weak property (${\beta}_{\kappa}$) and get the following strict implications. $$(UC){\Rightarrow}w-({\beta}_1){\Rightarrow}w-({\beta}_2){\Rightarrow}\;{\cdots}\;{\Rightarrow}w-({\beta}_{\infty}){\Rightarrow}(BS)$$.

• 충청수학회지
• /
• 제28권3호
• /
• pp.419-429
• /
• 2015

In this paper, we study properties SVEP, Bishop's property (${\beta}$), property (${\delta}$), decomposability, property $({\beta})_{\epsilon}$, subscalarity, Kato spectrum, generalized Kato decomposition, finite ascent for bounded linear operators in Banach spaces.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.161-168
• /
• 2006

In this paper, we study property (${\beta}$) and B-convexity in reflexive Banach spaces. It is shown that k-uniform convexity implies B-convexity and property (${\beta}$). We also show that there is a Banach space with property (${\beta}$) which cannot be equivalently renormed to be B-convex.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.459-468
• /
• 2011

Let T ${\in}$ L(X), S ${\in}$ L(Y), A ${\in}$ L(X, Y) and B ${\in}$ L(Y, X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares the same local spectral properties SVEP, Bishop's property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and and subscalarity. Moreover, the operators ${\lambda}I$ - T and ${\lambda}I$ - S have many basic operator properties in common.

• 폴리머
• /
• 제25권5호
• /
• pp.635-641
• /
• 2001

포접 기능을 가져 악취의 분리제거에 사용될 수 있을 것으로 보이는 $\beta$-시클로덱스트린 및 $\beta$-시클로덱스트린에 벤조산을 포접시킨 물질($\beta$-시클로덱스트린/벤조산 포접체)에 시아누르산 염화물을 반응시켜 클로로트리아진 유도체를 제조하고, 이를 면섬유와 반응시켜 새로운 소취 기능성 섬유를 제조하였다. 포접체의 형성은 적외선 분광분석 및 가시-자외선 분광분석기를 사용하여 확인하였으며, 반응기의 도입은 EDX로 확인하였다. 소취성능은 제조한 소취기능성 섬유를 컬럼에 채우고, 암모니아 기체를 흘려 보냈을 때 빠져나온 암모니아를 물에 용해시킨 용액의 농도를 0.1N 염산으로 적정하여 평가하였다. 섬유에 부착된 $\beta$-시클로덱스트린 단위가 증가할수록 소취성이 증가하였으며, $\beta$-시클로덱스트린에 벤조산을 포접한 경우에 소취성이 보다 증가하였다. 이는 포접체에 존재하는 벤조산과 암모니아의 결합때문이라고 생각되었다.

• 호남수학학술지
• /
• 제31권2호
• /
• pp.137-145
• /
• 2009

Let T ${\in}$ $\mathcal{L}$(X), S ${\in}$ $\mathcal{L}$(Y ), A ${\in}$ $\mathcal{L}$(X, Y ) and B ${\in}$ $\mathcal{L}$(Y,X) such that SA = AT, TB = BS, AB = S and BA = T. Then S and T shares that same local spectral properties SVEP, property (${\beta}$), property $({\beta})_{\epsilon}$, property (${\delta}$) and decomposability. From these common local spectral properties, we give some results related with Aluthge transforms and subscalar operators.

• Korean Journal of Mathematics
• /
• 제22권3호
• /
• pp.463-469
• /
• 2014

In this paper, we investigate relationship between superreflexivity and weak property (${\beta}_k$). Indeed, we get the following diagram.

• Journal of the Korean Data and Information Science Society
• /
• 제22권2호
• /
• pp.353-360
• /
• 2011

We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.487-496
• /
• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.