scholarly journals Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry

2014 ◽  
Vol 33 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Gary K. L. Tam ◽  
Ralph R. Martin ◽  
Paul L. Rosin ◽  
Yu-Kun Lai
Keyword(s):  
Local Isometry

EXTENDABILITY OF LOCAL ISOMETRY GROUPS

1989 ◽  
Vol 63 (1) ◽  
pp. 11-21
Author(s):  
V A Popov
Keyword(s):  
Isometry Groups ◽  
Local Isometry

scholarly journals On the semiduals of local isometry groups in three-dimensional gravity

2012 ◽  
Vol 53 (7) ◽  
pp. 073510 ◽  
Author(s):  
Prince K. Osei ◽  
Bernd J. Schroers
Keyword(s):  
Three Dimensional ◽  
Isometry Groups ◽  
Local Isometry ◽  
Dimensional Gravity

scholarly journals Skew Killing spinors in four dimensions

2021 ◽  
Author(s):  
Nicolas Ginoux ◽  
Georges Habib ◽  
Ines Kath
Keyword(s):  
Degenerate Case ◽  
Killing Spinor ◽  
Warped Products ◽  
Riemannian Product ◽  
Four Dimensions ◽  
Killing Spinors ◽  
Local Isometry ◽  
Spin Manifolds ◽  
Special Case

AbstractThis paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $$\psi $$ ψ is a spinor that satisfies the equation $$\nabla _X\psi =AX\cdot \psi $$ ∇ X ψ = A X · ψ with a skew-symmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the non-degenerate case, where the rank of A is four everywhere. We prove that in the degenerate case the manifold is locally isometric to the Riemannian product $${\mathbb {R}}\times N$$ R × N with N having a skew Killing spinor and we explain under which conditions on the spinor the special case of a local isometry to $${\mathbb {S}}^2\times {\mathbb {R}}^2$$ S 2 × R 2 occurs. In the non-degenerate case, the existence of skew Killing spinors is related to doubly warped products whose defining data we will describe.

scholarly journals Algebraic Reflexivity of Non-Canonical Isometries on Lipschitz Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1635
Author(s):  
Antonio Jiménez-Vargas ◽  
María Isabel Ramírez
Keyword(s):  
Isometry Group ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Integral Operators ◽  
Supremum Norm ◽  
Weighted Composition Operators ◽  
Local Isometry ◽  
Weighted Composition ◽  
Complex Valued ◽  
Linear Isometries

Let Lip([0,1]) be the Banach space of all Lipschitz complex-valued functions f on [0,1], equipped with one of the norms: fσ=|f(0)|+f′L∞ or fm=max|f(0)|,f′L∞, where ·L∞ denotes the essential supremum norm. It is known that the surjective linear isometries of such spaces are integral operators, rather than the more familiar weighted composition operators. In this paper, we describe the topological reflexive closure of the isometry group of Lip([0,1]). Namely, we prove that every approximate local isometry of Lip([0,1]) can be represented as a sum of an elementary weighted composition operator and an integral operator. This description allows us to establish the algebraic reflexivity of the sets of surjective linear isometries, isometric reflections, and generalized bi-circular projections of Lip([0,1]). Additionally, some complete characterizations of such reflections and projections are stated.

scholarly journals 2-LOCAL ISOMETRIES OF SOME OPERATOR ALGEBRAS

2002 ◽  
Vol 45 (2) ◽  
pp. 349-352 ◽  
Author(s):  
Lajos Molnár
Keyword(s):  
Operator Algebras ◽  
Linear Operators ◽  
Primary 47B49 ◽  
Similar Statement ◽  
Bounded Linear ◽  
C Algebra ◽  
Infinite Dimensional ◽  
C Algebras ◽  
Infinite Dimensional Hilbert Space ◽  
Local Isometry

AbstractAs a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras.AMS 2000 Mathematics subject classification: Primary 47B49

ON AUTOMORPHISMS OF LOCAL ISOMETRY GROUPS OF COMPACT ULTRAMETRIC SPACES

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1013-1024 ◽  
Author(s):  
YAROSLAV LAVRENYUK
Keyword(s):  
Transitive Group ◽  
Ultrametric Space ◽  
Isometry Groups ◽  
Ultrametric Spaces ◽  
Local Isometry

Completeness of the group of local isometries of compact ultrametric space is established for transitive group.

scholarly journals 2-локальные изометрии некоммутативных пространств Лоренца

2019 ◽  
Author(s):  
A.A. Alimov ◽  
V.I. Chilin
Keyword(s):  
Continuous Function ◽  
Von Neumann Algebra ◽  
Value Function ◽  
Linear Mapping ◽  
Singular Value ◽  
Linear Isometry ◽  
Von Neumann ◽  
Local Isometry ◽  
Measurable Operators ◽  
Finite Trace

Let mathcal M be a von Neumann algebra equipped with a faithful normal finite trace tau, and let Sleft( mathcalM, tauright) be an ast -algebra of all tau -measurable operators affiliated with mathcal M . For x in Sleft( mathcalM, tauright) the generalized singular value function mu(x):trightarrow mu(tx), t0, is defined by the equality mu(tx)infxp_mathcalM:, p2pp in mathcalM, , tau(mathbf1-p)leq t. Let psi be an increasing concave continuous function on 0, infty) with psi(0) 0, psi(infty)infty, and let Lambda_psi(mathcal M,tau) left x in Sleft( mathcalM, tauright): x _psi int_0inftymu(tx)dpsi(t) infty right be the non-commutative Lorentz space. A surjective (not necessarily linear) mapping V:, Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) is called a surjective 2-local isometry, if for any x, y in Lambda_psi(mathcal M,tau) there exists a surjective linear isometry V_x, y:, Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) such that V(x) V_x, y(x) and V(y) V_x, y(y). It is proved that in the case when mathcalM is a factor, every surjective 2-local isometry V:Lambda_psi(mathcal M,tau) to Lambda_psi(mathcal M,tau) is a linear isometry.

scholarly journals Analytic Extension of Riemannian Analytic Manifolds and Local Isometries

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1855
Author(s):  
Vladimir A. Popov
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Killing Vector ◽  
Necessary Condition ◽  
Analytic Extension ◽  
Analytic Manifold ◽  
Killing Vector Fields ◽  
Local Isometry ◽  
Stationary Subalgebra ◽  
Group Of Isometries

This article deals with a locally given Riemannian analytic manifold. One of the main tasks is to define its regular analytic extension in order to generalize the notion of completeness. Such extension is studied for metrics whose Lie algebra of all Killing vector fields has no center. The generalization of completeness for an arbitrary metric is given, too. Another task is to analyze the possibility of extending local isometry to isometry of some manifold. It can be done for metrics whose Lie algebra of all Killing vector fields has no center. For such metrics there exists a manifold on which any Killing vector field generates one parameter group of isometries. We prove the following almost necessary condition under which Lie algebra of all Killing vector fields generates a group of isometries on some manifold. Let g be Lie algebra of all Killing vector fields on Riemannian analytic manifold, h⊂g is its stationary subalgebra, z⊂g is its center and [g,g] is commutant. G is Lie group generated by g and is subgroup generated by h⊂g. If h∩(z+[g;g])=h∩[g;g], then H is closed in G.

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