Operators on indefinite inner product spaces

Embeddings, Operator Ranges, and Dirac Operators

“…If either inf n w + n = 0 or inf n w − n = 0 then 2 w is closely embedded, but not continuously, in 2 , with kernel operator M w −1 , the operator of multiplication with w −1 = (w −1 n ) in 2 . As a consequence of Proposition 3.3, Proposition 3.4 and the Lifting Theorem as in [8], we have a generalization, to the unbounded case, of the indefinite variant of the Lifting Theorem in [14] in the formulation of [18] …”

“…see [10]. Another motivation for these investigations comes from the works of de Branges [5] and Dritschel and Rovnyak [18] where operator spaces have been considered in the Kreȋn space setting. In [8] it was obtained an interpretation of the positive/negative energetic spaces associated to certain Dirac operators in terms of induced Kreȋn spaces, in the spirit of energy spaces of Friedrichs [20,21].…”

Krein-space operators determined by free product algebras induced by primes and graphs

“…Let H be a Hilbert space equipped with its (positive-de nite) inner product <, > H , i.e., it is the complete inner product space under the metric topology generated by the metric d H , [9], [10], [18], [19], [20] and cited papers therein.…”

Arithmetic Functions in Harmonic Analysis and Operator Theory

“…(14). Let .A; g p / be the arithmetic p-prime probability space, inducing the indefinite pseudo-inner product space .A; Q p /, where Q p is in the sense of (17).…”