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In the theory of Lebesgue type decompositions of linear relations (in particular linear operators) or of (pairs of) semibounded sesquilinear forms in a Hilbert space, the notion of a nonorthogonal decomposition of the Hilbert space plays an important role when the components of the Lebesgue-type decomposition are not mutually singular. This work offers a self-contained review of nonorthogonal Hilbert space decompositions in the context of operator range spaces and, in particular, of such decompositions in reproducing kernel Hilbert spaces.

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Nonorthogonal Hilbert Space Decompositions with Operator Range Spaces and Reproducing Kernel Hilbert Spaces

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  • 发表日期：

    2025年

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  • S. Hassi,
  • H. S. V. de Snoo

摘要

In the theory of Lebesgue type decompositions of linear relations (in particular linear operators) or of (pairs of) semibounded sesquilinear forms in a Hilbert space, the notion of a nonorthogonal decomposition of the Hilbert space plays an important role when the components of the Lebesgue-type decomposition are not mutually singular. This work offers a self-contained review of nonorthogonal Hilbert space decompositions in the context of operator range spaces and, in particular, of such decompositions in reproducing kernel Hilbert spaces.