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

Seppo Hassi () and Hendrik S. V. de Snoo ()
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Seppo Hassi: University of Vaasa, Department of Mathematics and Statistics
Hendrik S. V. de Snoo: University of Groningen, Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence

Chapter 9 in Operator Theory, 2026, pp 217-257 from Springer

Abstract: Abstract 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.

Keywords: Operator range; Operator range space; Pairs of operators; Sum of operator range spaces; Reproducing kernel space; Complementation; Overlapping space; Parallel sum; Nonorthogonal decomposition; Reproducing kernel Hilbert space; Embedding; Aroszajn decomposition; Normalized pair of contractions (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_118

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DOI: 10.1007/978-3-032-16356-1_118

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