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Calkin Representations of Unbounded Operator Algebras Acting on Non-Separable Domains

✍ Scribed by Klaus-Detlef Kürsten; Michael Milde

Publisher: John Wiley and Sons
Year: 1991
Tongue: English
Weight: 686 KB
Volume: 154
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19911540124

No coin nor oath required. For personal study only.

✦ Synopsis

There are constructed representations of unbounded operator algebras which generalize representations of B ( H ) constructed by J. W. CALKIN and H. BEHNCKE. For a large class of unitary spaces D, each uniformly closed two-sided ideal of the maximal Op*-algebra L + ( D ) appears as kernel of such a representation. Irreducibility of the representations is characterized in terms of properties of ultrafilters which define the representations.

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✍ Atsushi Inoue; Klaus-Detlef Kürsten 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 219 KB

The purpose of this paper is to study when a weight on an O U -algebra M M on a dense subspace D D in a Hilbert space H H is a trace weighted by a positive self-adjoint operator, that is, when there exists a positive self-adjoint operator ⍀