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# Compact and Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces with Applications to Boundary Eigenvalue Problems

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A selfadjoint operator A in a Krein space (K, [•, •]) is called deﬁnitizable if the resolvent set <... Weiterlesen
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## Beschreibung

A selfadjoint operator A in a Krein space (K, [•, •]) is called deﬁnitizable if the resolvent set ρ(A) is nonempty and there exists a polynomial p such that [p(A)x, x] ≥ 0 for all x ∈ dom (p(A)). It was shown in [L1] and [L5] that a deﬁnitizable operator A has a spectral function EA which is deﬁned for all real intervals the boundary points of which do not belong to some ﬁnite subset of the real axis. With the help of the spectral function the real points of the spectrum σ(A) of A can be classiﬁed in points of positive and negative type and critical points: A point μ ∈ σ(A) ∩ R is said to be of positive type (negative type) if μ is contained in some open interval δ such that EA(δ) is deﬁned and (EA(δ)K, [•, •]) (resp. (EA (δ)K, −[•, •])) is a Hilbert space. Spectral points of A which are not of deﬁnite type, that is, not of positive or negative type, are called critical points. The set of critical points of A is ﬁnite; every critical point of A is a zero of any polynomial p with the “deﬁnitizing” property mentioned above. Spectral points of positive and negative type can also be characterized with the help of approximative eigensequences (see [LcMM], [LMM], [J6]), which allows, in a convenient way, to carry over the sign type classiﬁcation of spectral points to non-deﬁnitizable selfadjoint operators and relations in Krein spaces.

## Produktinformationen

 Titel: Compact and Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces with Applications to Boundary Eigenvalue Problems EAN: 9783736914353 ISBN: 978-3-7369-1435-3 Format: E-Book (pdf) Herausgeber: Cuvillier Verlag Genre: Sonstiges Anzahl Seiten: 100 Veröffentlichung: 27.04.2005 Jahr: 2005