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Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
(Elsevier Science, 2021-08)
In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, ...
Metric geodesics of isometries in a Hilbert space and the extension problem
(American Mathematical Society, 2007-08)
We consider the problem of finding short smooth curves of isometries in a Hilbert space H. The length of a smooth curve γ(t), t ∈ [0, 1], is measured by means of ∫^1-0 γ^. (t)ǀǀ dt, where ǀǀ ǀǀ denotes the usual norm of ...
Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms
(Academic Press Inc Elsevier Science, 2020-03)
Consider the Lie group of n×n complex unitary matrices U(n) endowed with the bi-invariant Finsler metric given by the spectral norm, ‖X‖_U=‖U⁎X‖∞=‖X‖∞ for any X tangent to a unitary operator U. Given two points in U(n), ...
A note on geodesics of projections in the Calkin algebra
(Birkhauser Verlag Ag, 2020-11)
Let C(H) = B(H) / K(H) be the Calkin algebra (B(H) the algebra of bounded operators on the Hilbert space H, K(H) the ideal of compact operators, and π: B(H) → C(H) the quotient map), and PC(H) the differentiable manifold ...
Hopf-Rinow theorem in the Sato Grassmannian
(Academic Press Inc Elsevier Science, 2008-10)
Let U2 (H) be the Banach-Lie group of unitary operators in the Hilbert space H which are Hilbert-Schmidt perturbations of the identity 1. In this paper we study the geometry of the unitary orbit{u p u* : u ∈ U2 (H)}, of ...
Projections with fixed difference: a Hopf-Rinow theorem
(Elsevier Science, 2019-10)
The set D_A0 , of pairs of orthogonal projections (P,Q) in generic position with fixed difference P−Q=A_0, is shown to be a homogeneous smooth manifold: it is the quotient of the unitary group of the commutant {A_0}′ divided ...
Representation by triples of algebras with an MV-retract
(Elsevier B.V., 2019-08)
We introduce the notion of generalized rotation of a residuated lattice and characterize the varieties of bounded residuated lattices they generate, which we name MVR n . These algebras have a retraction onto a hyperarchimedean ...
Some links between identifying codes and separating, dominating and total dominating sets in graphs
(Elsevier, 2015-12)
In the search for a dynamic programming-based algorithm derived from the modular decomposition of graphs, we analyze the behavior of the identifying code number under disjoint union and join operations. This study lead us ...
Lagrangian Grassmannian in infinite dimension
(Elsevier Science, 2009-03)
Given a complex structure J on a real (finite or infinite dimensional) Hilbert space H, we study the geometry of the Lagrangian Grassmannian Λ (H) of H, i.e. the set of closed linear subspaces L ⊂ H such that J (L) = L⊥. ...
Grassmann geometry of zero sets in reproducing kernel Hilbert spaces
(Academic Press Inc Elsevier Science, 2021-08)
Let H be a reproducing kernel Hilbert space of functions on a set X. We study the problem of finding a minimal geodesic of the Grassmann manifold of H that joins two subspaces consisting of functions which vanish on given ...