Given two chains of subspaces in C, the set of those unitary matrices is studied that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U − In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, a formula for the minimum value ‖U − In‖ is given, and the set of all the unitary matrices in the set attaining the mini...

Given two chains of subspaces in C, we study the set of unitary matrices that map the subspaces in the first chain onto the corresponding subspaces in the second chain, and minimize the value ‖U− In‖ for various unitarily invariant norms ‖ · ‖ on Cn×n. In particular, we give formula for the minimum value ‖U − In‖, and describe the set of all the unitary matrices in the set attaining the minimum...

For a square system of analytic equations, a Newton-invariant subspace is a set which contains the resulting point of a Newton iteration applied to each point in the subspace. For example, if the equations have real coefficients, then the set of real points form a Newtoninvariant subspace. Starting with any point for which Newton’s method quadratically converges to a solution, this article uses...

We show that there are obstructions to the existence of certain types of invariant subspaces of the Milnor monodromy; this places restrictions on the cohomology of Milnor fibres of non-isolated hypersurface singularities.

We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, oo) which is/7-convex for some/? > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if ...