• Title/Summary/Keyword: Maximal ideal space

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The Structure of Maximal Ideal Space of Certain Banach Algebras of Vector-valued Functions

  • Shokri, Abbas Ali;Shokri, Ali
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.189-195
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    • 2014
  • Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

The Maximal Ideal Space of Extended Differentiable Lipschitz Algebras

  • Abolfathi, Mohammad Ali;Ebadian, Ali
    • Kyungpook Mathematical Journal
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    • v.60 no.1
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    • pp.117-125
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    • 2020
  • In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

ON COVERING AND QUOTIENT MAPS FOR 𝓘𝒦-CONVERGENCE IN TOPOLOGICAL SPACES

  • Debajit Hazarika;Ankur Sharmah
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.267-280
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    • 2023
  • In this article, we show that the family of all 𝓘𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘𝒦-convergence and the relationship between 𝓘𝒦-continuity and 𝓘𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘𝒦-sequential space.

PRIMARY IDEALS IN THE RING OF COTINUOUS FUNCTIONS

  • Bae, Soon Sook
    • Kyungpook Mathematical Journal
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    • v.18 no.1
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    • pp.105-107
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    • 1978
  • Considering the prime z-filters on a topological space X through the structures of the ring C(X) of continuous functions. a prime z-filter is uniquely determined by a primary z-ideal in the ring C(X), i. e., they have a one-to-one correspondence. Any primary ideal is contained in a unique maximal ideal in C(X). Denoting $\mathfrak{F}(X)$, $\mathfrak{Q}(X)$, 𝔐(X) the prime, primary-z, maximal spectra, respectively, $\mathfrak{Q}(X)$ is neither an open nor a closed subspace of $\mathfrak{F}(X)$.

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APPROXIMATION IN LIPSCHITZ ALGEBRAS OF INFINITELY DIFFERENTIABLE FUNCTIONS

  • Honary, T.G.;Mahyar, H.
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.629-636
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    • 1999
  • We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

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THE CORONA THEOREM FOR BOUNDED FUNCTIONS IN DIRICHLET SPACE

  • Nah, Young-Chae
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.141-146
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    • 1997
  • In this paper we prove that the corona theorem for the algebra $H^{\infty}(D){\cap}D(D)$. That is, we prove that $\mathcal{M}{\setminus}{\overline{D}}$ is an empty set where $\mathcal{M}$ is the maximal ideal space of the given algebra.

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On the Existence of Maximal Fan Design

  • Kim, Hyoungsoon;Park, Dongkwon;Kim, KyungHee
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.347-354
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    • 2002
  • An n-point design is maximal fan if all the models with n-terms satisfying the divisibility condition are estimable. Such designs tend to be space filling and look very similar to the ″Latin-hypercube″ designs used in computer experiments. Caboara, Pistone, Riccomago and Wynn (1997) conjectured that a maximal fan design on an integer grid exists for any n and m, where m is the number of factors. In this paper we examine the relationship between maximal fan design and latin-hypercube to give a partial solution for the conjecture.

AN IDEAL-BASED ZERO-DIVISOR GRAPH OF 2-PRIMAL NEAR-RINGS

  • Dheena, Patchirajulu;Elavarasan, Balasubramanian
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.6
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    • pp.1051-1060
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    • 2009
  • In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

Performance of space -time coding for four transmit antennas on Rayleigh fading channel (4개의 송신 안테나를 사용하는 5-T 방식의 Rayleigh fading에서의 성능)

  • 이은옥;이혁재
    • Proceedings of the IEEK Conference
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    • 2002.06a
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    • pp.41-44
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    • 2002
  • Alamouti proposes a two branch transmit diver-sity scheme that provides the same diversity order as maximal ratio combining at the receiver. It has many advantages of no bandwidth expansion, not requiring channel information at the transmitter and simple maximum likelihood decoding at the receiver. Papadias and Foschini extend this sch-eme to four transmit antennas and suggest several schemes to decrease the interference component and allow the attainment of the open-loop capacity. This paper shows the performance of ZF and MM-SE schemes comparing with ideal case on 4xl sy-stem over BER and 10% outage capacity.

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AN IDEAL - BASED ZERO-DIVISOR GRAPH OF POSETS

  • Elavarasan, Balasubramanian;Porselvi, Kasi
    • Communications of the Korean Mathematical Society
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    • v.28 no.1
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    • pp.79-85
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    • 2013
  • The structure of a poset P with smallest element 0 is looked at from two view points. Firstly, with respect to the Zariski topology, it is shown that Spec(P), the set of all prime semi-ideals of P, is a compact space and Max(P), the set of all maximal semi-ideals of P, is a compact $T_1$ subspace. Various other topological properties are derived. Secondly, we study the semi-ideal-based zero-divisor graph structure of poset P, denoted by $G_I$ (P), and characterize its diameter.