IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Proper subspaces and compatibility
Autor/es:
ANDRUCHOW ESTEBAN; DI IORIO Y LUCERO, EUGENIA; CHIUMIENTO EDUARDO
Revista:
STUDIA MATHEMATICA
Editorial:
POLISH ACAD SCIENCES INST MATHEMATICS
Referencias:
Lugar: VARSOVIA; Año: 2016 vol. 231 p. 195 - 195
ISSN:
0039-3223
Resumen:
Let E be a Banach space contained in a Hilbert space L. Assume thatthe inclusion is continuous with dense range. Following the terminology of Gohberg andZambicki, we say that a bounded operator on E is a proper operator if it admits anadjoint with respect to the inner product of L. A proper operator which is self-adjointwith respect to the inner product of L is called symmetrizable. By a proper subspace Swe mean a closed subspace of E which is the range of a proper projection. Furthermore,if there exists a symmetrizable projection onto S, then S belongs to a well-known class ofsubspaces called compatible subspaces. We nd equivalent conditions to describe propersubspaces. Then we prove a necessary and sucient condition for a proper subspace tobe compatible. The existence of non-compatible proper subspaces is related to spectralproperties of symmetrizable operators. Each proper subspace S has a supplement T whichis also a proper subspace.We give a characterization of the compatibility of both subspacesS and T . Several examples are provided that illustrate dierent situations between properand compatible subspaces