Abstract
The first and second representation theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the associated operators is determined for special cases. This extends results by Grubišić et al. (Mathematika 59:169–189, 2013).
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Daultray R., Lions J.L.: Mathematical Analysis and Numerical Methods for Science and Technology Volume 3 Spectral Theory and Applications. Springer, Berlin (1990)
Fleige A., Hassi S., Snoo H.S.V., Winkler H.: Non-semibounded closed symmetric forms associated with a generalized Friedrichs extension. Proc. R. Soc. Edinb. Sect. A 144, 1–15 (2014)
Grubišić L., Kostrykin V., Makarov K.A., Veselić K.: Representation theorems for indefinite quadratic forms revisited. Mathematika 59, 169–189 (2013)
Kostrykin V., Makarov K.A., Motovilov A.K.: A generalization of the \({\tan 2\theta}\) theorem. Oper. Theory Adv. Appl. 149, 349–372 (2004)
Kato T.: Perturbation Theory for Linear Operators. Springer, Berlin (1966)
McIntosh A.: Bilinear forms in Hilbert space. J. Math. Mech. 19, 1027–1045 (1970)
Nenciu G.: Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms. Commun. Math. Phys. 48, 235–247 (1976)
Schmitz, S.: Representation theorems for indefinite quadratic forms and applications. Dissertation, Johannes Gutenberg-Universität Mainz (2014)
Schmüdgen K.: Unbounded Self-adjoint Operators on Hilbert Space. Springer, Dordrecht (2012)
Sohr H.: The Navier–Stokes Equations: An Elementary Functional Analytic Approach. Birkhäuser, Basel (2001)
Veselić K.: Spectral perturbation bounds for selfadjoint operators I. Oper. Matrices 2, 307–340 (2008)
Weidmann J.: Lineare Operatoren auf Hilberträumen Teil I Grundlagen. Teubner, Stuttgart (2000)
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Schmitz, S. Representation Theorems for Indefinite Quadratic Forms Without Spectral Gap. Integr. Equ. Oper. Theory 83, 73–94 (2015). https://doi.org/10.1007/s00020-015-2252-3
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DOI: https://doi.org/10.1007/s00020-015-2252-3