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category of Hilbert spaces (Definition)
Definition 0.1   The category $\mathcal{H}ilb_f$ of finite-dimensional Hilbert spaceshttp://physicslibrary.org/encyclopedia/NormInducedByInnerProduct.html is defined as the category whose objects are all finite-dimensional Hilbert spaces $\mathcal{H}_f$, and whose morphisms are linear maps between $\mathcal{H}_f$ spaces. The isomorphisms in $\mathcal{H}ilb_f$ are all isometric isomorphisms.

Furthermore, one also has the following, general definition for any Hilbert space.

Definition 0.2   The category $\mathcal{H}ilb$ of Hilbert spaces is defined as the category whose objects are all Hilbert spaces $\mathcal{H}$, and whose morphisms are linear maps between $\mathcal{H}$ spaces. The isomorphisms in $\mathcal{H}ilb$ are all isometric isomorphisms.
Remark 0.1  

The category of $\mathcal{H}ilb$ Hilbert spaces has direct sums and is a Cartesian category.



"category of Hilbert spaces" is owned by bci1.
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Keywords:  Hilbert spaces, category

Cross-references: general definition, isomorphisms, morphisms, objects, Hilbert spaces, category
There are 7 references to this object.

This is version 1 of category of Hilbert spaces, born on 2009-02-04.
Object id is 496, canonical name is CategoryOfHilbertSpaces.
Accessed 492 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
 03.65.Fd (Algebraic methods )
Pending Errata and Addenda
None.
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