INVESTIGADORES
GIRIBET Juan Ignacio
artículos
Título:
On Frames for Krein Spaces
Autor/es:
JUAN IGNACIO GIRIBET; ALEJANDRA MAESTRIPIERI; FRANCISCO MARTÍNEZ PERÍA; PEDRO MASSEY
Revista:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Año: 2012 vol. 393 p. 122 - 137
ISSN:
0022-247X
Resumen:
A definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(HH, K{,}{,})$ is in particular a frame for $HH$ in the Hilbert space sense. But it is also compatible with the indefinite inner product $K{,}{,}$, meaning that it determines a maximal uniformly $J$-positive and a maximal uniformly $J$-negative subspace, an analogue to the maximal dual pair associated to a $J$-orthonormal basis. Also, each $J$-frame induces an indefinite reconstruction formula for the vectors in $HH$, which resembles the one given by a $J$-orthonormal basis.
