In this paper, we introduce the concept of orthogonal frames in Krein spaces, prove independence choice fundamental symmetry, and from this, obtain a number interesting properties that they satisfy. We show there is no distinction between space its associated Hilbert. Furthermore, characterize dual to given frame, which useful tool for constructing examples.

We give an example of a positive operator B in a Krein space with the following properties: the nonzero spectrum of B consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of B are uniformly bounded and the point ∞ is a singular critical point of B. An operator A in the Krein space (K, [ · , · ]) is said to be positive ...

Introduction. Let 77 be a Hubert space and let D be a closed proper subspace of 77. Let 70 be a linear contraction on D to 77. The problem of characterizing the contractions on all of 77 which extend J0 is directly related to the extension problems for unbounded transformations posed and treated by M. G. Krein [2] and R. S. Phillips [3]. In §1 of this paper we establish the following solution o...

Abstract In this article, it is shown that Koebe inner functions and squares of singular Nevanlinna functions, so called atomic density have minimal realizations in reproducing kernel Krein spaces.

In the present paper we construct and solve a differential model for the q-analog of the Plancherel growth process. The construction is based on a deformation of the Makrov-Krein correspondence between continual diagrams and probability distributions.

We present natural (invariant) definite and indefinite scalar products on the N = 1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical framework.