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Polar decomposition under perturbations of the scalar product.

Corach, Gustavo; Maestripieri, Alejandra; Stojanoff, Demetrio — 2000

ELA. The Electronic Journal of Linear Algebra [electronic only]

Operator inequalities, geodesics and interpolation

Gustavo Corach — 1994

Banach Center Publications

Extension of characters in commutative Banach algebras

Gustavo Corach; Fernando Suárez — 1987

Studia Mathematica

Total curvature of non-differentiable curves.

Gustavo Corach; Horacio Porta — 1987

Revista Matemática Iberoamericana

Metrics in the set of partial isometries with finite rank

Esteban Andruchow; Gustavo Corach — 2005

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $I_{(\infty)}$ be the set of partial isometries with finite rank of an infinite dimensional Hilbert space $H$ . We show that $I_{(\infty)}$ is a smooth submanifold of the Hilbert space $B_{2} (H)$ of Hilbert-Schmidt operators of $H$ and that each connected component is the set $I_{N}$ , which consists of all partial isometries of rank $N < \infty$ . Furthermore, $I_{(\infty)}$ is a homogeneous space of $U_{(\infty)} \times U_{(\infty)}$ , where $U_{(\infty)}$ is the classical Banach-Lie group of unitary operators of $H$ , which are Hilbert-Schmidt perturbations of the identity. We introduce two Riemannian metrics...

Geometry of oblique projections

E. Andruchow; Gustavo Corach; D. Stojanoff — 1999

Studia Mathematica

Let A be a unital C*-algebra. Denote by P the space of selfadjoint projections of A. We study the relationship between P and the spaces of projections $P_{a}$ determined by the different involutions $_{a}$ induced by positive invertible elements a ∈ A. The maps $φ : P \to P_{a}$ sending p to the unique $q \in P_{a}$ with the same range as p and $Ω_{a} : P_{a} \to P_{a}$ sending q to the unitary part of the polar decomposition of the symmetry 2q-1 are shown to be diffeomorphisms. We characterize the pairs of idempotents q,r ∈ A with ||q-r|| < 1 such that...

A note on the differentiable structure of generalized idempotents

Esteban Andruchow; Gustavo Corach; Mostafa Mbekhta — 2013

Open Mathematics

For a fixed n > 2, we study the set Λ of generalized idempotents, which are operators satisfying T n+1 = T. Also the subsets Λ†, of operators such that T n−1 is the Moore-Penrose pseudo-inverse of T, and Λ*, of operators such that T n−1 = T* (known as generalized projections) are studied. The local smooth structure of these sets is examined.

A classification of projectors

Gustavo Corach; Alejandra Maestripieri; Demetrio Stojanoff — 2005

Banach Center Publications

A positive operator A and a closed subspace of a Hilbert space ℋ are called compatible if there exists a projector Q onto such that AQ = Q*A. Compatibility is shown to depend on the existence of certain decompositions of ℋ and the ranges of A and $A^{1 / 2}$ . It also depends on a certain angle between A() and the orthogonal of .

Characterization of Bessel sequences.

M. Laura Arias; Gustavo Corach; Miriam Pacheco — 2007

Extracta Mathematicae

Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and (H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {e} of H, a bijection α: (H) → L(H) can be defined. The aim of this paper is to characterize α (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.

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