Representations of Hermitian Kernels by Means of Krein Spaces

  • Tiberiu Constantinescu

    University of Texas at Dallas, United States
  • Aurelian Gheondea

    Bilkent University, Bilkent, Ankara, Turkey


Hermitian kernels are studied as generalizations of kernels of positive type. The main tool is the axiomatic concept of induced Krem space. The existence of Kolmogorov decompositions of a hermitian kernel and their uniqueness, modulo unitary equivalence, are characterized. The existence of reproducing kernel Krein spaces is shown to be equivalent to the existence of Kolmogorov decompositions. Applications Applications to the Naimark dilations of Toeplitz hermitian kernels on the set of integers and to the uniqueness of the Krem space completions of nondegenerate inner product spaces are included.

Cite this article

Tiberiu Constantinescu, Aurelian Gheondea, Representations of Hermitian Kernels by Means of Krein Spaces. Publ. Res. Inst. Math. Sci. 33 (1997), no. 6, pp. 917–951

DOI 10.2977/PRIMS/1195144882