Dual systems of inductive-projective limits of Hilbert spaces originating from self-adjoint operators

S.J.L. Eijndhoven, van; J. Graaf, de; P. Kruszynski

doi:10.1016/1385-7258(85)90040-X

Dual systems of inductive-projective limits of Hilbert spaces originating from self-adjoint operators

S.J.L. Eijndhoven, van, J. Graaf, de, P. Kruszynski

Center for Analysis, Scientific Computing and Applications

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Abstract

In this paper we construct spaces SF( ) and TF( ) where F denotes a suitable directed set of Borel functions on n, and where denotes an n-tuple of strongly commuting self-adjoint operators. The spaces SF( ) and TF( ) are in duality. We give conditions on the set F such that SF( ) and TF( ) can be described both as a (non-strict) inductive limit and as a projective limit of Hilbert spaces. Examples are included.

Original language	English
Pages (from-to)	277-297
Journal	Indagationes Mathematicae (Proceedings)
Volume	88
Issue number	3
DOIs	https://doi.org/10.1016/1385-7258(85)90040-X
Publication status	Published - 1985

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abstract = "In this paper we construct spaces SF( ) and TF( ) where F denotes a suitable directed set of Borel functions on n, and where denotes an n-tuple of strongly commuting self-adjoint operators. The spaces SF( ) and TF( ) are in duality. We give conditions on the set F such that SF( ) and TF( ) can be described both as a (non-strict) inductive limit and as a projective limit of Hilbert spaces. Examples are included.",

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AB - In this paper we construct spaces SF( ) and TF( ) where F denotes a suitable directed set of Borel functions on n, and where denotes an n-tuple of strongly commuting self-adjoint operators. The spaces SF( ) and TF( ) are in duality. We give conditions on the set F such that SF( ) and TF( ) can be described both as a (non-strict) inductive limit and as a projective limit of Hilbert spaces. Examples are included.

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DO - 10.1016/1385-7258(85)90040-X

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JO - Indagationes Mathematicae (Proceedings)

JF - Indagationes Mathematicae (Proceedings)

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ER -

Dual systems of inductive-projective limits of Hilbert spaces originating from self-adjoint operators

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