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

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

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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Copyright 2008 Elsevier B.V., All rights reserved.

Cite this

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AU - de Graaf, J.

AU - Kruszyński, P.

PY - 1985

Y1 - 1985

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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JF - Indagationes Mathematicae

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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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