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Subjects
46-XX Functional analysis
46Jxx Commutative Banach algebras and commutative topological algebras
46J25 Representations of commutative topological algebras

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On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem

Jorma Arhippainen, Jukka Kauppi (2013)

Studia Mathematica

We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.

On the algebra of smooth operators

Tomasz Ciaś (2013)

Studia Mathematica

Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.

Currently displaying 1 – 2 of 2

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