Spectrum of J-frame operators Giribet, Juan Langer, Matthias Leben, Leslie Maestripieri, Alejandra Martínez Pería, Francisco Trunk, Carsten article article article Text https://doi.org/10.7494/OpMath.2018.38.5.623 https://www.db-thueringen.de/receive/dbt_mods_00043200 http://uri.gbv.de/document/gvk:ppn:1025538935 doc-type:Article ScholarlyArticle ddc:510 frame -- Krein space -- block operator matrix -- spectrum A J-frame is a frame F for a Krein space (H, [·, ·]) which is compatible with the indefinite inner product [·, ·] in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H. With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H. The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2 × 2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2 × 2 block representation. Moreover, this 2 × 2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator. 2018 electronic resource remote Computermedien Online-Ressource 27 Seiten eng Opuscula mathematica -- 2300-6919 -- http://uri.gbv.de/document/gvk:ppn:518959600 -- 2254303-X public https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess