A new metric in the study of shift invariant subspaces of L^2(R^n) - Harish, V. K.; Balasubramani, M. S. (Methods of Functional Analysis and Topology, 2012)
A new metric on the set of all shift invariant subspaces of L^2(R^n) is defined and the properties are studied. The limit of a sequence of principal shift invariant subspaces under this metric is principal shift invariant is proved. Also, the uniform convergence of a sequence of local trace functions is characterized in terms of convergence under this new metric.