$H i l b$ category of Hilbert spaces

Definition 0.1.

The category $\\mathcal{H}ilb_{f}$ of finite-dimensional Hilbert spaces 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.

单词	HilbCategoryOfHilbertSpaces
释义	$H i l b$ category of Hilbert spaces Definition 0.1. The category $\\mathcal{H}ilb_{f}$ of finite-dimensional Hilbert spaces 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.
随便看	utility Vacuous vacuous Valency valency Valuation valuation ValuationDeterminedByValuationDomain valuation determined by valuation domain ValuationDomain valuation domain ValuationDomainIsLocal valuation domain is local ValuationRingOfAField valuation ring of a field ValueGroupOfCompletion value group of completion ValueOfDirichletEtaFunctionAtS2 value of Dirichlet eta function at s=2 ValueOfRiemannZetaFunctionAtS4 value of Riemann zeta function at s=4 ValueOfTheRiemannZetaFunctionAtS0 value of the Riemann zeta function at s=0 ValueOfTheRiemannZetaFunctionAtS2 value of the Riemann zeta function at s=2

H⁢i⁢l⁢b category of Hilbert spaces

Definition 0.1.

Definition 0.2.

Remark 0.1.

$H i l b$ category of Hilbert spaces