On the spectrum of J-frame operators

FRANCISCO MARTÍNEZ PERÍA

Berlin

Workshop; New Methods in Extension Theory applied to Quantum Mechanics; 2016

Weierstrass Institute for Applied Analysis and Stochastics

Recently, J-frame where introduced in order to extend Hilbert space frame theory to Krein spaces. Given a Krein space H, a J-frame is a family of vectors F={f_i}_i, composed of positive and negative vectors,which spans a pair of maximal uniformly definite subspaces. For each J-frame F there is an associated operator S : H → H, selfadjoint with respect to the Krein space structure, which allows to reconstruct any vector of the Krein space as a (possibly infinite) linear combination of the vectors in F. Along this talk, we present a spectral description of J-frame operators.It is based in a joint work with Juan I. Giribet, M. Langer, L. Leben, A. Maestripieri, and C. Trunk.