Rearrangement Invariant Orthogonal Sums in Krein Spaces. II

Fuente: arXiv
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Main Authors: Dritschel, Michael A., Maestripieri, Alejandra, Rovnyak, James
Format: Preprint
Published: 2025
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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
id 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