• Title/Summary/Keyword: locally convex space

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A Maximal Element of Condensing Multimaps

  • Kim, Won Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.6 no.1
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    • pp.59-64
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    • 1993
  • In this note, we shall give a maximal element existence theorem for condensing multimaps in a locally convex Hausdorff topological vector space.

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ALGEBRAS OF GELFAND-CONTINUOUS FUNCTIONS INTO ARENS-MICHAEL ALGEBRAS

  • Oubbi, Lahbib
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.585-602
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    • 2019
  • We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

COMMON FIXED POINT THEOREM AND INVARIANT APPROXIMATION IN COMPLETE LINEAR METRIC SPACES

  • Nashine, Hemant Kumar
    • East Asian mathematical journal
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    • v.28 no.5
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    • pp.533-541
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    • 2012
  • A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED SPACES OF VECTOR-VALUED ANALYTIC FUNCTIONS

  • Manhas, Jasbir Singh
    • Journal of the Korean Mathematical Society
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    • v.45 no.5
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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.

METRIZABILITY AND SUBMETRIZABILITY FOR POINT-OPEN, OPEN-POINT AND BI-POINT-OPEN TOPOLOGIES ON C(X, Y)

  • Barkha, Barkha;Prasannan, Azhuthil Raghavan
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.905-913
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    • 2022
  • We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

A UNIFIED FIXED POINT THEORY OF MULTIMAPS ON TOPOLOGICAL VECTOR SPACES

  • Park, Seh-Ie
    • Journal of the Korean Mathematical Society
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    • v.35 no.4
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    • pp.803-829
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    • 1998
  • We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

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SUBSERIES CONVERGENCE AND SEQUENCE-EVALUATION CONVERGENCE

  • Cho, Min-Hyung;Hwang, Hong Taek;Yoo, Won Sok
    • Korean Journal of Mathematics
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    • v.6 no.2
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    • pp.331-339
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    • 1998
  • We show a series of improved subseries convergence results, e.g., in a sequentially complete locally convex space X every weakly $c_0$-Cauchy series on X must be $c_0$-convergent. Thus, if X contains no copy of $c_0$, then every weakly $c_0$-Cauchy series on X must be subseries convergent.

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CHARACTERIZATIONS OF BOUNDED VECTOR MEASURES

  • Ronglu, Li;Kang, Shin-Min
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.209-215
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    • 2000
  • Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

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DISTRIBUTIONAL FRACTIONAL POWERS OF SIMILAR OPERATORS WITH APPLICATIONS TO THE BESSEL OPERATORS

  • Molina, Sandra Monica
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1249-1269
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    • 2018
  • This paper provides a method to study the nonnegativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and nonnegative, we can study the complex powers using an appropriate locally convex space. In this case, the initial operator also will be nonnegative and we will be able to study its powers. In particular, we have applied this method to Bessel-type operators.