000K  utf8
0100  876733372
1100  2017$c2017-01-04
1500  eng
2050  urn:nbn:de:gbv:ilm1-2017200016
3000  Giribet, Juan
3010  Langer, Matthias
3010  Leben, Leslie
3010  Maestripieri, Alejandra
3010  Martinez Peria, Francisco
3010  Trunk, Carsten
4000  Spectrum of J-frame operators  [Giribet, Juan]
4060  20 Seiten
4209  A J-frame is a frame F for a Krein space which is compatible with the indefinite inner product in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in H . With every J-frame the so-called J-frame operator is associated, which is a self-adjoint operator in the Krein space H . The J-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of J-frame operators in a Krein space by a 2X2 block operator representation. The J-frame bounds of F are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the 2X2 block representation. Moreover, this 2X2 block representation is utilized to obtain enclosures for the spectrum of J-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all J-frames associated with a given J-frame operator.
4950  https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2017200016$xR$3Volltext$534
4961  http://uri.gbv.de/document/gvk:ppn:876733372
5051  510
5550  block operator matrix
5550  Frame
5550  Krein space
5550  spectrum