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Non-Commutative Weak*-Continuous Operator Extensions
Başlık:
Non-Commutative Weak*-Continuous Operator Extensions
Yazar:
Flores, Luis Carlos, author.
ISBN:
9780438002012
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (46 pages)
Genel Not:
Source: Masters Abstracts International, Volume: 57-06M(E).
Advisors: Beate G. Zimmer Committee members: David P. Blecher; George D. Tintera.
Özet:
Extension theorems such as the Hahn-Banach Extension Theorem are a central idea of functional analysis. In 1962, Gleason and Whitney proved an extension theorem for weak*-continuous, linear functionals on H infinity(D) to positive, weak*-continuous functionals on Linfinity (T). Hoffman and Rossi in 1967 provided a related, albeit different, extension theorem: weak*-continuous characters on a unital subalgebra A of L infinity (T) can be extended to positive functionals on Linfinity (T). They demonstrated that A + A* being weak*-dense in H infinity (D) was not necessary for a weak*-continuous character to have a positive, weak*-continuous extension.
Arveson is credited with a non-commutative version of the Hahn-Banach Extension Theorem: a completely positive, linear map from a unital, self-adjoint subspace X of a C*-algebra A into B(H), where H is an arbitrary Hilbert space, can be extended to a completely positive map from A into B(H).
In this work, we look at the methods Hoffman and Rossi used to develop their extension theorem, and investigate if they can be used in a non-commutative setting. We provide a non-commutative generalization of their Extended Krein-Smulian Theorem, which was a central part of their proof. We also demonstrate that some special subalgebras of the non-commutative space, M2 (Linfinity( m)) will have weak*-continuous functionals on them with weak*-continuous and positive extensions on all of M2 ( Linfinity (m)). Furthermore, we generalize the work of Hoffman and Rossi in a non-commutative fashion to some weak*-continuous characters on singly generated dual algebras.
Notlar:
School code: 1417
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(691922.1) | 691922-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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