Isometries on Orthogonal Sums of Kreĭn Spaces

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Isometries on Kreĭn spaces admit a Wold-type decomposition into a unitary part and an internal shift under specific regularity conditions, and their minimal unitary extensions can be characterized by the convergence of associated orthogonal projections. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Dan Popovici

doi:10.1007/s00020-026-02860-y

August 21, 2026Integral Equations and Operator TheoryOpen Access

Isometries on Orthogonal Sums of Kreĭn Spaces

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Key Points

To investigate isometries, internal direct sums, and unitary extensions on orthogonal sums of Kreĭn spaces and regular subspaces.
Introduced internal sums (i-sums) and internal shifts (i-shifts) for pairwise orthogonal regular subspaces associated with fundamental symmetries.
Formulated operator conditions for unitary equivalence to shifts on Hardy-type Kreĭn spaces.
Analyzed minimal unitary extensions on Kreĭn spaces using convergence properties of operator projection sequences.
Proved a Wold-type decomposition theorem that splits Kreĭn space isometries into a unitary part and an internal shift under regularity conditions.
Characterized multiplication operators between external and internal sums via uniform norm boundedness of component restrictions.
Established criteria under which minimal unitary extensions of Kreĭn space isometries exhibit bilateral shift structures.

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Implication

Theoretical analysis characterizes isometries and internal shifts on orthogonal sums of Kreĭn spaces, establishing a Wold-type decomposition theorem for indefinite inner product spaces.

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Dan Popovici (2026) studied this question.

synapsesocial.com/papers/6a8aad977677a34114445c83 https://doi.org/10.1007/s00020-026-02860-y

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Isometries on Orthogonal Sums of Kreĭn Spaces

Key Points

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Implication

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Cite This Study

Isometries on Orthogonal Sums of Kreĭn Spaces

Key Points

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Implication

Discussion

Cite This Study

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