𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The structure of compact disjointness preserving operators on continuous functions

✍ Scribed by Ying-Fen Lin; Ngai-Ching Wong

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
183 KB
Volume
282
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Let T be a compact disjointness preserving linear operator from C~0~(X) into C~0~(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Σ~n~ δ ⊗h~n~ for a (possibly finite) sequence {x~n~ }~n~ of distinct points in X and a norm null sequence {h~n~ }~n~ of mutually disjoint functions in C~0~(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

On the Analytic Continuation of the Mina
On the Analytic Continuation of the Minakshisundaram–Pleijel Zeta Function for Compact Symmetric Spaces of Rank One
✍ Roberto Camporesi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 310 KB

We give two equivalent analytic continuations of the Minakshisundaram᎐Pleijel Ž . zeta function z for a Riemannian symmetric space of the compact type of U r K rank one UrK. First we prove that can be written as Ž . function for GrK the noncompact symmetric space dual to UrK , and F z is an Ž Ž . .