On an Ideal in Algebras of Unbounded Operators

✍ Scribed by W. Timmermann

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 504 KB
• Volume: 91
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19790910127

✦ Synopsis

The closure of the set of finite dimensional operators of a+@) with respect to different topologies is oonaidered. The obtained ideals have many properties similar to those of the idcal of completely continuous operatom on ~E B T space. For example, under some appropriate aesumpt.ione all oontinuous functionals are normal, irreducible representations arc equivalent to the identical reprecwntation and so on.

In this paper we continue the considerations of [123 and refer to this paper for gened remarks on the subject. We concentrate our attention on the closure of the ideal of finite dimensional opemtors of 5?+( 9) with respect to different topologiw. The ideals obtained in this way reflect many properties of the ideal of completely continuous opemtors in H I L J ~~T space. For example, the dual space can be identified with a certain idea.1 of trace oIaw operators, irreducible representations are (under some natural restriotions) equivalent to the identical representakion and so on.