Spectrum of J-frame operators

• Autorzy: Giribet J. , Langer M. , Leben L. , Maestripieri A. , Peria F. M. , Trunk C.

Identyfikatory

DOI

10.7494/OpMath.2018.38.5.623

• Języki publikacji: EN

Abstrakty

EN

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 x 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 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.

Słowa kluczowe

EN

frame; Krein space; block operator matrix; spectrum

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 5
• Strony: 623--649
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Giribet J.

• Facultad de Ingenieria, Universidad de Buenos Aires Paseo Colon 850, (1063) Buenos Aires, Argentina
• Instituto Argentino de Matematica "Alberto P. Calderón" (CONICET) Saavedra 15, Piso 3, (1083) Buenos Aires, Argentina

autor

Langer M.

• University of Strathclyde Department of Mathematics and Statistics 26 Richmond Street, Glasgow Gl 1XH, United Kingdom

autor

Leben L.

• Technische Universitat Ilmenau Institut fur Mathematik Postfach 100565, D-98684 Ilmenau, Germany

autor

Maestripieri A.

• Facultad de Ingenieria, Universidad de Buenos Aires Paseo Colon 850, (1063) Buenos Aires, Argentina
• Instituto Argentino de Matematica "Alberto P. Calderón" (CONICET) Saavedra 15, Piso 3, (1083) Buenos Aires, Argentina

autor

Peria F. M.

• Centro de Matematica de La Plata (CeMaLP), Facultad de Ciencias Exactas Universidad Nacional de La Plata, C.C. 172, (1900) La Plata, Argentina
• Instituto Argentino de Matematica "Alberto P. Calderón" (CONICET) Saavedra 15, Piso 3, (1083) Buenos Aires, Argentina

autor

Trunk C.

• Instituto Argentino de Matematica "Alberto P. Calderón" (CONICET) Saavedra 15, Piso 3, (1083) Buenos Aires, Argentina
• Technische Universitat Ilmenau Institut fur Mathematik Postfach 100565, D-98684 Ilmenau, Germany

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).