• Title/Summary/Keyword: Isometries

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GEOMETRIC CLASSIFICATION OF ISOMETRIES ACTING ON HYPERBOLIC 4-SPACE

  • Kim, Youngju
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.303-317
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    • 2017
  • An isometry of hyperbolic space can be written as a composition of the reflection in the isometric sphere and two Euclidean isometries on the boundary at infinity. The isometric sphere is also used to construct the Ford fundamental domains for the action of discrete groups of isometries. In this paper, we study the isometric spheres of isometries acting on hyperbolic 4-space. This is a new phenomenon which occurs in hyperbolic 4-space that the two isometric spheres of a parabolic isometry can intersect transversally. We provide one geometric way to classify isometries of hyperbolic 4-space using the isometric spheres.

GENERALIZATIONS OF ALESANDROV PROBLEM AND MAZUR-ULAM THEOREM FOR TWO-ISOMETRIES AND TWO-EXPANSIVE MAPPINGS

  • Khodaei, Hamid;Mohammadi, Abdulqader
    • Communications of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.771-782
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    • 2019
  • We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

STABILITY OF ISOMETRIES ON RESTRICTED DOMAINS

  • Jung, Soon-Mo;Kim, Byung-Bae
    • Journal of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.125-137
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    • 2000
  • In the present paper, the classical results of the stability of isometries obtained by some authors will be generalized; More precisely, the stability of isometries on restricted (unbounded or bounded) domains will be investigated.

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POSETS ADMITTING THE LINEARITY OF ISOMETRIES

  • Hyun, Jong Youn;Kim, Jeongjin;Kim, Sang-Mok
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.3
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    • pp.999-1006
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    • 2015
  • In this paper, we deal with a characterization of the posets with the property that every poset isometry of $\mathbb{F}^n_q$ fixing the origin is a linear map. We say such a poset to be admitting the linearity of isometries. We show that a poset P admits the linearity of isometries over $\mathbb{F}^n_q$ if and only if P is a disjoint sum of chains of cardinality 2 or 1 when q = 2, or P is an anti-chain otherwise.

ISOMETRIES OF (2)}_{2n}$

  • Park, Taeg-Young
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.609-620
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    • 1995
  • In this paper, we introduce the generalization $A^{(2)}_{2n}$ of tridiagonal algebras $A_{2n}$ and investigate the isometries of such algebras.

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ISOMETRIES ON THE SPACE OF CONTINUOUS FUNCTIONS WITH FINITE CODIMENSIONAL RANGE

  • HEDAYATIAN, K.
    • Honam Mathematical Journal
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    • v.27 no.4
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    • pp.631-639
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    • 2005
  • For compact Hausdorff spaces X and Y let C(X) and C(Y) denote the complex Banach spaces of complex valued continuous functions on X and Y, respectively. Also let $T:C(X){\rightarrow}C(Y)$ be a linear isomerty. Necessary and sufficient conditions are given such that range of T has finite codimension.

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A SIMPLE ALGEBRA GENERATED BY INFINITE ISOMETRIES AND REPRESENTATIONS

  • Jeong, Eui-Chai
    • Communications of the Korean Mathematical Society
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    • v.14 no.1
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    • pp.157-169
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    • 1999
  • We consider the C\ulcorner-algebra O\ulcorner generated by infinite isometries \ulcorner,\ulcorner, …on Hilbert spaces with the property \ulcorner \ulcorner$\leq$1 for every n$\in$N. We present certain type of representations of C\ulcorner-algerbra O\ulcorner on a separable Hilbert space and study the conditions for irreducibility of these representations.

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WEAK NORMAL PROPERTIES OF PARTIAL ISOMETRIES

  • Liu, Ting;Men, Yanying;Zhu, Sen
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1489-1502
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    • 2019
  • This paper describes when a partial isometry satisfies several weak normal properties. Topics treated include quasi-normality, subnormality, hyponormality, p-hyponormality (p > 0), w-hyponormality, paranormality, normaloidity, spectraloidity, the von Neumann property and Weyl's theorem.

DISCUSSIONS ON PARTIAL ISOMETRIES IN BANACH SPACES AND BANACH ALGEBRAS

  • Alahmari, Abdulla;Mabrouk, Mohamed;Taoudi, Mohamed Aziz
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.485-495
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    • 2017
  • The aim of this paper is twofold. Firstly, we introduce the concept of semi-partial isometry in a Banach algebra and carry out a comparison and a classification study for this concept. In particular, we show that in the context of $C^*$-algebras this concept coincides with the notion of partial isometry. Our results encompass several earlier ones concerning partial isometries in Hilbert spaces, Banach spaces and $C^*$-algebras. Finally, we study the notion of (m, p)-semi partial isometries.