Rearrangement Invariant Orthogonal Sums in Krein Spaces. II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918356669431808 |
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| author | Dritschel, Michael A. Maestripieri, Alejandra Rovnyak, James |
| author_facet | Dritschel, Michael A. Maestripieri, Alejandra Rovnyak, James |
| contents | Part I of the paper considered infinite orthogonal sums of regular subspaces in a Krein space (that is, of subspaces which are themselves Krein spaces). How precisely these sums should be defined and conditions for when such a sum is itself regular were examined. These included, for example, a boundedness condition for the sum of the corresponding orthogonal projections. The same problem is addressed here for (quasi-)pseudo-regular subspaces. Such subspaces happen to be the orthogonal direct sum of a regular space and an isotropic, or neutral, subspace. Alternate characterizations of such subspaces are given, and infinite orthogonal sums are examined via unconditional, or Moore-Smith, sums of operator ranges. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_15428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rearrangement Invariant Orthogonal Sums in Krein Spaces. II Dritschel, Michael A. Maestripieri, Alejandra Rovnyak, James Functional Analysis 47B50, 47A05, 46C20 Part I of the paper considered infinite orthogonal sums of regular subspaces in a Krein space (that is, of subspaces which are themselves Krein spaces). How precisely these sums should be defined and conditions for when such a sum is itself regular were examined. These included, for example, a boundedness condition for the sum of the corresponding orthogonal projections. The same problem is addressed here for (quasi-)pseudo-regular subspaces. Such subspaces happen to be the orthogonal direct sum of a regular space and an isotropic, or neutral, subspace. Alternate characterizations of such subspaces are given, and infinite orthogonal sums are examined via unconditional, or Moore-Smith, sums of operator ranges. |
| title | Rearrangement Invariant Orthogonal Sums in Krein Spaces. II |
| topic | Functional Analysis 47B50, 47A05, 46C20 |
| url | https://arxiv.org/abs/2509.15428 |