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Existence of well-behaved ∗-representations of locally convex ∗-algebras

✍ Scribed by S. J. Bhatt; M. Fragoulopoulou; A. Inoue

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
242 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The following problems are investigated: (1) The existence of well‐behaved ∗︁‐representations on a ∗︁‐algebra 𝒜 equipped with an unbounded m *‐seminorm p , in terms of non‐zero p ‐continuous representable (positive) linear functionals on the domain 𝔇(p ) of p . (2) The existence of well‐behaved ∗︁‐representations of a locally convex ∗︁‐algebra 𝒜, in terms of non‐zero unbounded C *‐seminorms on 𝒜 with domain the ∗︁‐subalgebra 𝒜~b~ generated by the hermitian part of the Allan bounded set 𝒜~0~ of 𝒜. (3) The existence of faithful well‐behaved ∗︁‐representations of a locally convex ∗︁‐algebra 𝒜, in terms of the so‐called unbounded Gel'fand–Naĭmark C *‐seminorm on 𝒜. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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