Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. II
Abstract
Abstract 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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Finite Group Theory Research
Publication details
- Journal / source
- Complex Analysis and Operator Theory
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 3
- Publication date
- 25 February 2026
- Language
- EN