Rearrangement Invariant Orthogonal Sums in Krein Spaces. II

Abstract

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.