Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T17:59:31.246Z Has data issue: false hasContentIssue false
  • English
  • Français

A JORDAN-LIKE DECOMPOSITION IN THE NONCOMMUTATIVE SCHWARTZ SPACE

Part of: Topological (rings and) algebras with an involution Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  15 December 2014

KRZYSZTOF PISZCZEK
KRZYSZTOF PISZCZEK*
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, ul. Umultowska 87, 61-614 Poznań, Poland email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that every continuous self-adjoint functional on the noncommutative Schwartz space can be decomposed into a difference of two positive functionals. Moreover, this decomposition is minimal in the natural sense.

Keywords

Fréchet space(Fréchet) LMC-algebrapositive functionalself-adjoint functionalJordan decomposition

MSC classification

Primary: 46K05: General theory of topological algebras with involution
Secondary: 46H05: General theory of topological algebras 46H35: Topological algebras of operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 322 - 330
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Bost, J.-B., ‘Principe d’Oka, K-théorie et systèmes dynamiques non commutatifs’, Invent. Math. 101(2) (1990), 261–333.Google Scholar
Ciaś, T., ‘On the algebra of smooth operators’, Studia Math. 218(2) (2013), 145–166.CrossRefGoogle Scholar
Cuntz, J., ‘Cyclic theory and the bivariant Chern–Connes character’, in: Noncommutative Geometry, Lecture Notes in Mathematics, 1831 (Springer, Berlin, 2004), 73–135.Google Scholar
Dales, H. G., Banach Algebras and Automatic Continuity, London Mathematical Society Monographs. New Series, 24 (Clarendon Press and Oxford University Press, New York, 2000), Oxford Science.Google Scholar
Domański, P., ‘Algebra of smooth operators’, http://main3.amu.edu.pl/∼domanski/salgebra1.pdf.Google Scholar
Elliott, G. A., Natsume, T. and Nest, R., ‘Cyclic cohomology for one-parameter smooth crossed products’, Acta Math. 160(3–4) (1988), 285–305.CrossRefGoogle Scholar
Jarchow, H., Locally Convex Spaces, Mathematische Leitfäden [Mathematical Textbooks] (Teubner, Stuttgart, 1981).CrossRefGoogle Scholar
Meise, R. and Vogt, D., Introduction to Functional Analysis, Oxford Graduate Texts in Mathematics, 2 (Clarendon Press and Oxford University Press, New York, 1997), translated from the German by M. S. Ramanujan and revised by the authors.Google Scholar
Phillips, N. C., ‘K-theory for Fréchet algebras’, Internat. J. Math. 2(1) (1991), 77–129.CrossRefGoogle Scholar
Pirkovskii, A. Yu., ‘Flat cyclic Fréchet modules, amenable Fréchet algebras, and approximate identities’, Homology Homotopy Appl. 11(1) (2009), 81–114.Google Scholar
Piszczek, K., ‘Automatic continuity and amenability in the noncommutative Schwartz space’, submitted.Google Scholar
Schweitzer, L. B., ‘Spectral invariance of dense subalgebras of operator algebras’, Internat. J. Math. 4(2) (1993), 289–317.Google Scholar