Positive operators in the functional calculus
Abstract
We address the question of which functions are positive on all positive operators on Banach lattices. Necessary and sufficient conditions are established which characterize when polynomials are positive on all positive 2 x 2 matrices. We also characterize which analytic functions are positive on all positive operators on infinite dimensional Banach lattices. Geometric criteria are given establishing which matrices which are similar to positive matrices. It is also shown that in low dimensions, the collection of matrices which are similar to positive matrices is closed.
Degree
Ph.D.
Advisors
Burkinshaw, Purdue University.
Subject Area
Mathematics
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