4 papers
Closing in on the kernel of an operator between Banach spaces
Douglas S. Bridges
This note deals with the question: If T is a linear mapping between Banach spaces X and Y, and x belongs to X and has small norm, is x close to the kernel of T? It draws on notions…
Z-stability in Constructive Analysis
Douglas Bridges, James Dent, Maarten McKubre-Jordens
We introduce Z-stability, a notion capturing the intuition that if a function f maps a metric space into a normed space and if the norm of f(x) is small, then x is close to a zero…
Locating Ax, where A is a subspace of B(H)
Douglas Suth Bridges
Let A be a linear space of operators on a Hilbert space H, x a vector in H, and Ax the subspace of H comprising all vectors of the form Tx with T in A. We discuss, within a Bishop-…
Precompact Apartness Spaces
Douglas S Bridges
We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one.…