• Title, Summary, Keyword: continuity

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CONTINUITY OF (α,β)-DERIVATIO OF OPERATOR ALGEBRAS

  • Hou, Chengjun;Meng, Qing
    • Journal of the Korean Mathematical Society
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    • v.48 no.4
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    • pp.823-835
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    • 2011
  • We investigate the continuity of (${\alpha},{\beta}$)-derivations on B(X) or $C^*$-algebras. We give some sufficient conditions on which (${\alpha},{\beta}$)-derivations on B(X) are continuous and show that each (${\alpha},{\beta}$)-derivation from a unital $C^*$-algebra into its a Banach module is continuous when and ${\alpha}$ ${\beta}$ are continuous at zero. As an application, we also study the ultraweak continuity of (${\alpha},{\beta}$)-derivations on von Neumann algebras.

SOME STRONG FORMS OF (g,g')-CONTINUITY ON GENERALIZED TOPOLOGICAL SPACES

  • Min, Won-Keun;Kim, Young-Key
    • Honam Mathematical Journal
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    • v.33 no.1
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    • pp.85-91
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    • 2011
  • We introduce and investigate the notions of super (g,g')-continuous functions and strongly $\theta$(g,g')-continuous functions on generalized topological spaces, which are strong forms of (g,g')-continuous functions. We also investigate relationships among such the functions, (g,g')-continuity and (${\delta},{\delta}'$)-continuity.

WEAKLY WELL-DECOMPOSABLE OPERATORS AND AUTOMATIC CONTINUITY

  • Cho, Tae-Geun;Han, Hyuk
    • Journal of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.347-365
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    • 1996
  • Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

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ON SLIGHTLY $\alpha$-CONTINUOUS FUNCTIONS

  • Chae, G.I.;Noiri, T.;Kim, J.S.
    • East Asian mathematical journal
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    • v.19 no.2
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    • pp.241-249
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    • 2003
  • In [11] the feeble continuity is introduced and then the weak and strong forms of feeble(or, equivalently $\alpha$-continuity) continuity are studied. In this note, we introduce a type of function called a slightly $\alpha$-continuous function and study several properties of it

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INTUITIONISTIC FUZZY FUNCTIONS

  • Hanafy, I.M.
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.2
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    • pp.200-205
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    • 2003
  • In this paper, we generally introduce some of the terminology of Yalvac [10] and Azad [4] in intuitionistic fuzzy topological spaces. In addition to the fundamental concepts of intuitionistic fuzzy sets, we emphasize the usefulness of the concepts of intuitionistic fuzzy points intuitionistic fuzzy elementhood. Mainly, this paper is devoted to the study of intuitionistic fuzzy topological spaces with specific attention to the weaker forms of fuzzy continuity.

ON WEAKLY sγ-CONTINUOUS FUNCTIONS

  • Min, Won Keun
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.3
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    • pp.353-358
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    • 2009
  • In [6], the author introduced the concepts of $s\gamma$-open sets and $s\gamma$-continuous functions. In this paper, we introduce the concept of weak $s\gamma$-continuity which is a generalization of $s\gamma$-continuity and weak continuity and investigate characterizations for such functions.

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