118 research outputs found
Geometry of positive operators and uhlmann's approach to the geometric phase
No full textIn Uhlmann's description of the differential geometry of the space Ω of density operators, a relevant role is played by the parallel condition w*w =w*w, where w is a lifting of acurve y in Ω, i.e. w(t)o(t)* = y(t) for all t. In this paper we get a principal bundle with a natural connection over the space G + of all positive invertible elements of a C*-algebra such that the parallel transport is ruled by Uhlmann's parallel equation.Fil: Corach, Gustavo. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentin
Polar decomposition under perturbations of the scalar product
No full textLet A be a unital C*-algebra with involution * represented in a Hilbert space H, G the group of invertible elements of A, U the unitary group of A, G^s the set of invertible selfadjoint elements of A, Q= ξ ∈ G : ξ ^2 = 1 the space of reflectionsand P = Q ∩ U. For any positive a ∈ G consider the a-unitary group U_a ={ g ∈ G : a^-1 g^* a = g ^-1}, i.e. the elements which are unitary with respect to the scalar product ⟨ ξ,n ⟩ a = ⟨ a ξ,n ⟩ for ξ, n ∈ H. If π denotes the map that assigns to each invertible element its unitary part in the polar decomposition, it is shown that the restriction π |_Ua : Ua →U is a diffeomorphism, that π ( ua ∩ Q) = P and that π (Ua ∩ G^s ) = Ua ∩ G^s = { u ∈ G : u = u^* = u^-1 and au = ua }.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentin
The Poincaré half-space of a C∗-algebra
No full textLet A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature.Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simon Bolivar.; Venezuel
On the geometry of generalized inverses
No full textWe study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, inside S lies a copy the set I of partial isometries, we prove that this set is a C∞ submanifold of S (as well as a submanifold of A). These manifolds carry actions from, respectively, G_A × G_A and U_A ×U_A, where G_A is the group of invertibles of A and U_A is the subgroup of unitary elements. These actions define homogeneous reductive structures for S and I (in the differential geometric sense). Certain topological and homotopical properties of these sets are derived. In particular, it is shown that if A is a von Neumann algebra and p is a purely infinite projection of A, then the connected component I_p of p in I is simply connected. If 1 − p is also purely infinite, then I_p is contractible.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Mbekhta, Mostafa. Universite Lille; Franci
Are DNA Test Infallible?
No full textModern technology has strongly influenced most fields of knowledge and forensic sciences do not escape this reality. With the advent of the application of molecular biology to human identification by means of DNA typing, conceptual conflicts were introduced. After over 15 years of worldwide experience, the robustness and reliability of DNA analysis was demonstrated. However in Latin America, judges, prosecutors and defenders, due in part to different educational background as compared to scientists, may ignore potential restrictions concerning DNA profiling results. Since its beginnings, DNA testing was surrounded by an aura of infallibility. Nowadays, a big number of highly polymorphic genetic markers, included in commercial kits, as well as automated devices for DNA extraction and purification, PCR amplification, electrophoresis and data analysis are available. Nevertheless, errors may occur. This work describes the main causes for errors in DNA testing in forensic laboratories that simultaneously processes hundreds or thousands of samples a month and makes suggestions to prevent each particular problem. It is important to underscore that DNA testing should be considered one more piece of evidence within the context of a criminal or forensic investigation, and that the judicial sentences should be based on the evidence as a whole and not just on the genetic studies.Fil: Penacino, G.. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Microbiología, Inmunología y Biotecnología. Cátedra de Genética y Biología Molecular; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Sala, Adriana Andrea. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Microbiología, Inmunología y Biotecnología. Cátedra de Genética y Biología Molecular; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; ArgentinaFil: Corach, Daniel. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Departamento de Microbiología, Inmunología y Biotecnología. Cátedra de Genética y Biología Molecular; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentin
Lifting properties in operator ranges
No full textGiven a bounded positive linear operator A on a Hilbert space H we consider the semi-Hilbertian space (H, _A), where _A =. On the other hand, we consider the operator range R(A^1/2) with its canonical Hilbertian structure, denoted by R(A^1/2). In this paper we explore the relationship between different types of operators on (H, _A) with classical subsets of operators on R(A^1/2), like Hermitian, normal, contractions, projections, partial isometries and so on. We extend a theorem by M. G. Krein on symmetrizable operators and a result by M. Mbekhta on reduced minimum modulus.Fil: Arias, Maria Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Gonzalez, Maria Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
Routine Y-STR typing in forensic casework
No full textIn the field of molecular diagnosis, forensic casework analysis is one of the most demanding investigations, due to its social impact. Optimization of DNA typing multiplex reactions with identical cycling conditions as those required by autosomal short tandem repeats (STR) multiplex reduces errors, and saves time and reagents. Previously, we validated a five Y-STRs set, all of them generating single band patterns. This work reports the optimization of combined multiplexes, a triplex (DYS19, DYS390 and DYS391) and a duplex (DYS392 and DYS393), that can be amplified in identical cycling conditions as those required by commercially available multiplex autosomal STR kits. In addition both Y chromosome multiplexes can be combined for co-injection on a capillary electrophoresis based automated sequencer. Statistical attributes of the haplotypes of the five Y-STR investigated were evaluated in unrelated males from different metropolitan areas of Argentina. This system was successfully used for investigating more than 350 forensic routine cases in our country.Fil: Corach, Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Filgueira Risso, Lucas. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Marino, Miguel Eduardo. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; ArgentinaFil: Penacino, Gustavo. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; ArgentinaFil: Sala, Adriana Andrea. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica. Servicio de Huellas Digitales Genéticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay; Argentin
The Grassmann manifold of a Hilbert space
No full textThe present paper surveys the geometric properties of the Grassmann manifold Gr(H ) of an infinite dimensional complex Hilbert space H . Gr(H ) is viewed as a set of operators, identifying each closed subspace S ⊂ H with the orthogonal projection PS onto S . Most of the results surveyed here were stated by G. Corach, H. Porta and L. Recht: submanifold structure, homogeneous reductive structure, local minimality of geodesics. Some recent results concerning the existence and uniqueness of a geodesic joining two given projections, which were obtained by the present author, are also presented.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaXII Congreso Antonio MonteiroBahía BlancaArgentinaConsejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanc
Redundant decompositions, angles between subspaces and oblique projections
No full textLet Η be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S _l_ of S and the closure of AS. We show that every redundant decomposition H = S+M_l_ (where redundant means that S ∩M_l_ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory
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