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category of Hilbert spaces
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(Definition)
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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.
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"category of Hilbert spaces" is owned by bci1.
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Cross-references: direct sums, isometric isomorphisms, isomorphisms, linear maps, morphisms, objects, Hilbert spaces, finite-dimensional, category
There are 2 references to this entry.
This is version 5 of category of Hilbert spaces, born on 2008-09-22, modified 2009-01-26.
Object id is 11070, canonical name is CategoryOfHilbertSpaces.
Accessed 1201 times total.
Classification:
| AMS MSC: | 18-00 (Category theory; homological algebra :: General reference works ) | | | 46E20 (Functional analysis :: Linear function spaces and their duals :: Hilbert spaces of continuous, differentiable or analytic functions) | | | 46C15 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Characterizations of Hilbert spaces) | | | 46C50 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Generalizations of inner products ) | | | 46C05 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Hilbert and pre-Hilbert spaces: geometry and topology ) | | | 46K15 (Functional analysis :: Topological algebras with an involution :: Hilbert algebras) |
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Pending Errata and Addenda
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