Abstract
In this chapter, some basic concepts of O-families are developed, and the graph topologies of O-families are studied in detail. An O-family is a set of closable linear operators defined on a common (dense) domain in a Hilbert space which contains the identity map. By means of the graph seminorms, each O-family A gives rise to a locally convex topology on its domain, the graph topology of A. The corresponding locally convex space is denoted by A D A . Most of the material in this chapter is directly related to the graph topology.
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Additional References
Ascoli, R., Epifanio, G., and Restivo, A. [1] On the mathematical description of quantized fields. Commun. Math. Phys. 18 (1970), 291 to 300.
Lassner, G. and Timmermann, W. [2] Normal states on algebras of unbounded operators. Rep. Math. Phys. 3 (1972), 295 – 305.
Junek, H. [1] Locally Convex Spaces and Operator Ideals. Teubner-Texte. Vol. 56, B. G. Teubner, Leipzig, 1983.
Brooks, R. M. [1] Some algebras of unbounded operators. Math. Nachr. 56 (1973), 47–62.
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© 1990 Springer Basel AG
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Schmüdgen, K. (1990). O-Families and Their Graph Topologies. In: Unbounded Operator Algebras and Representation Theory. Operator Theory: Advances and Applications, vol 37. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7469-4_2
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DOI: https://doi.org/10.1007/978-3-0348-7469-4_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7471-7
Online ISBN: 978-3-0348-7469-4
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