IAM 02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Schmidt decomposable products of projections
Autor/es:
ANDRUCHOW, ESTEBAN; CORACH, GUSTAVO
Revista:
INTEGRAL EQUATIONS AND OPERATOR THEORY
Editorial:
BIRKHAUSER VERLAG AG
Referencias:
Lugar: BASEL; Año: 2017 vol. 89 p. 557 - 580
ISSN:
0378-620X
Resumen:
We characterize operators T = PQ (P,Q orthogonal projec5tions in a Hilbert space H) which have a singular value decomposition. 16 A spatial characterizations is given: this condition occurs if and only7 if there exist orthonormal bases {n} of R(P) and {n} of R(Q) such8 that n, m = 0 if n = m. Also it is shown that this is equivalent9 to A = P − Q being diagonalizable. Several examples are studied, re10lating Toeplitz, Hankel and Wiener?Hopf operators to this condition.11 We also examine the relationship with the differential geometry of the12 Grassmann manifold of underlying the Hilbert space: if T = PQ has13 a singular value decomposition, then the generic parts of P and Q are14 joined by a minimal geodesic with diagonalizable exponent.
