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Updated: Nov 21, 2025
08:51
Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers
Published on: August 18, 2017
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Co-actions, Isometries, and isomorphism classes of Hilbert modules.
1University of New Brunswick at Fredericton, Fredericton, E3B 5A3 Canada.
Advances in Operator Theory
|January 14, 2021
Summary
This study demonstrates that A-linear maps of Hilbert A-modules are equivalent to unitary operators under specific conditions. This finding aids in classifying Hilbert modules over quantum groups and understanding co-actions.
Area of Science:
- Functional Analysis
- Operator Algebras
- Quantum Groups
Background:
- Hilbert modules are generalizations of Hilbert spaces.
- Unitary operators are fundamental in quantum mechanics and functional analysis.
- Multiplicative unitaries and quantum groups are advanced topics in mathematical physics.
Purpose of the Study:
- To establish conditions for A-linear maps in Hilbert A-modules to be induced by unitary operators.
- To apply these findings to the theory of multiplicative unitaries and quantum groups.
- To develop a theoretical framework for analyzing co-actions and their properties.
Main Methods:
- Characterization of A-linear maps via extensions to enveloping Hilbert spaces.
- Application of multiplicative unitary theory.
- Utilizing the Cuntz semigroup functor.
Main Results:
- An A-linear map of Hilbert A-modules is induced by a unitary Hilbert module operator if and only if it extends to an ordinary unitary on enveloping Hilbert spaces.
- Computation of equivalence classes of Hilbert modules over C*-algebraic quantum groups.
- Demonstration that the Cuntz semigroup functor maps co-actions to multiplicative actions.
Conclusions:
- The developed theory provides tools for proving the non-existence of certain co-actions.
- Establishes a connection between co-actions and multiplicative actions via the Cuntz semigroup functor.
- Advances the understanding of Hilbert modules in the context of quantum groups.
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