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

S. J.L. van Eijndhoven; J. de Graaf; P. Kruszyński

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

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

Center for Analysis, Scientific Computing and Applications

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Abstract

In this paper we construct spaces S_Φ(A) and T_Φ(A) where Φ denotes a suitable directed set of Borel functions on Rⁿ, and where A denotes an n-tuple of strongly commuting self-adjoint operators. The spaces S_Φ(A) and T_Φ(A) are in duality. We give conditions on the set Φ such that S_Φ(A) and T_Φ(A) 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
Number of pages	21
Journal	Indagationes Mathematicae
Volume	47
Issue number	3
Publication status	Published - 1985

Bibliographical note

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Cite this

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N2 - In this paper we construct spaces SΦ(A) and TΦ(A) where Φ denotes a suitable directed set of Borel functions on Rn, and where A denotes an n-tuple of strongly commuting self-adjoint operators. The spaces SΦ(A) and TΦ(A) are in duality. We give conditions on the set Φ such that SΦ(A) and TΦ(A) can be described both as a (non-strict) inductive limit and as a projective limit of Hilbert spaces. Examples are included.

AB - In this paper we construct spaces SΦ(A) and TΦ(A) where Φ denotes a suitable directed set of Borel functions on Rn, and where A denotes an n-tuple of strongly commuting self-adjoint operators. The spaces SΦ(A) and TΦ(A) are in duality. We give conditions on the set Φ such that SΦ(A) and TΦ(A) 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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ER -

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

Abstract

Bibliographical note

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