Mathematics Commons^™

Pseudocontinuations And The Backward Shift, William T. Ross, Alexandru Aleman, Stefan Richter

Department of Math & Statistics Faculty Publications

In this paper, we will examine the backward shift operator Lf = (f −f(0))/z on certain Banach spaces of analytic functions on the open unit disk D. In particular, for a (closed) subspace M for which LM Ϲ M, we wish to determine the spectrum, the point spectrum, and the approximate point spectrum of L│M. In order to do this, we will use the concept of “pseudocontinuation" of functions across the unit circle T.

We will first discuss the backward shift on a general Banach space of analytic functions and then for the weighted …

Approximation Of Compact Homogeneous Maps, John R. Hubbard

Department of Math & Statistics Faculty Publications

Within the clasp of continuous homogeneous maps between Banach spaces, it is proved that every compact map can be uniformly approximated by finite-rank maps. This result is obtained by means of the classical metric projection on Banach spaces.