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Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. II

Lookup NU author(s): Dr Michael DritschelORCiD

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Abstract

© The Author(s) 2026.Part I of the paper considered infinite orthogonal sums of regular subspaces in a Kreĭn space (that is, of subspaces which are themselves Kreĭn spaces). How precisely these sums should be defined and conditions for when such sums are themselves regular were determined. 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 are orthogonal direct sums of a regular space and isotropic, or neutral, subspaces. Alternate characterizations of such subspaces are given, and infinite orthogonal sums are examined via unconditional, or Moore-Smith, sums of operator ranges.

Publication metadata

Author(s): Dritschel MA, Maestripieri A, Rovnyak J

Publication type: Article

Publication status: Published

Journal: Complex Analysis and Operator Theory

Year: 2026

Volume: 20

Issue: 3

Online publication date: 25/02/2026

Acceptance date: 24/01/2026

Date deposited: 09/03/2026

ISSN (print): 1661-8254

ISSN (electronic): 1661-8262

Publisher: Springer International Publishing

URL: https://doi.org/10.1007/s11785-026-01914-8

DOI: 10.1007/s11785-026-01914-8

Data Access Statement: No datasets were generated or analysed during the current study

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