What is the differene between Rigid Hilbert Space and Hilbert Space?

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What is the difference between Rigid Hilbert Space and Hilbert Space?
 
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I guess you mean rigged Hilbert space.

http://www.abhidg.net/RHSclassreport.pdf

http://arxiv.org/abs/quant-ph/0502053
The role of the rigged Hilbert space in Quantum Mechanics
Authors: R. de la Madrid
(Submitted on 9 Feb 2005)
Abstract: There is compelling evidence that, when continuous spectrum is present, the natural mathematical setting for Quantum Mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in Quantum Mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.
 
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Thank you very much Tom.Stoer , indeed I also found the following text about Rigged Hilbert Space by Arno Bohm, The Rigged Hilbert Space and Quantum Mechanics.
 

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