Index

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Index

Subindex

: see amplification
: see axioms
: see bilinear mapping
: see C ${\;\!}^*$ -algebra
: see completelely bounded mapping
: see examples
: see Haagerup tensor product
: see Hilbertian operator space
: see injective op. space tensor product
: see lemma of
: see mapping
: see mapping space
: see module homomorphism
: see multilinear mapping
: see operator algebra
: see operator module
: see operator space
: see operator space tensor product
: see projective op. space tensor product
: see special operator spaces
: see theorem of

absolutely matrix convex

Matrix convexity

absolutely matrix convex combination

Matrix convexity

abstract operator space

see operator space

algebra homomorphism

Operator algebras

amplification

The mappings |

bilinear mapping: see bilinear mapping
joint: see bilinear mapping

automatic complete boundedness

Automatic Complete Boundedness

axioms

of Ruan

operator module: Operator modules
operator space: The spaces

bilinear mapping

amplification

Operator algebras | |

to quadratic matrices $\Phi^{(n)}$: Amplification
to rectangular matrices $\Phi^{(n,l)}$: Amplification

completely bounded

Operator algebras | see Haagerup tensor product | | Complete boundedness

norm ${ \left\Norm \cdot \right\Norm }_{\mathrm{cb}}$: Complete boundedness
norm on th level $\Vert\Phi\Vert _n$: Complete boundedness
representation: Representation
space $\mathit{CB}(X \times Y; Z)$: Complete boundedness
transposition: Complete boundedness

joint amplification

$\Phi^{(p \times q)}$: Amplification
matrix duality

jointly completely bounded

see projective operator space tensor product | | Completely bounded bilinear mappings | Jointly complete boundedness

norm ${ \left\Norm \cdot \right\Norm }_{\mathrm{jcb}}$: Jointly complete boundedness
space $\mathit{JCB}(X \times Y; Z)$: Jointly complete boundedness
transposition: Jointly complete boundedness

linearization $\tilde\Phi$

Amplification

transposed mapping $\Phi^t$

Jointly complete boundedness

transposed mapping $\Phi^t$

Complete boundedness

bipolar theorem

Bipolar theorems

Calkin algebra

Completely bounded module homomorphisms

$\mathit{CB}$ -ideal property

Mapping Spaces

$\mathit{CB}$ -mapping space

Mapping Spaces

characterization

completely locally reflexive operator spaces: Complete Local Reflexivity

Christensen

theorem of: Completely Bounded Multilinear Mappings

column Hilbert space

see hilbertian operator space

column norm

Characterizations

complete quotient mapping

see completely bounded mapping

completely bounded mapping

The mappings | |

complete quotient mapping: The mappings
completely contractive: The mappings
completely isometric: The mappings

completely contractive

see completely bounded mapping

completely isometric

see completely bounded mapping | The adjoint operator

completely locally reflexive

Complete Local Reflexivity

concrete operator space

see operator space

convex combination

absolutely matrix convex combination: Matrix convexity
matrix convex combination: Matrix convexity

cross norm

cross norms

-algebra

Examples | Multiplicative Structures | Operator algebras |

commutative: Examples | Construction of $\mathit{MIN}$ : | Examples
injective: Completely bounded module homomorphisms
nuclear: Examples
quasi-cyclic: Automatic Complete Boundedness

decomposition theorem

for completely bounded symmetric multilinear mappings: Completely Bounded Multilinear Mappings
for self-adjoint completely bounded bimodule homomorphisms: Completely bounded module homomorphisms
of Tomiyama-Takesaki: Completely bounded module homomorphisms

derivations

completely bounded: Completely Bounded Multilinear Mappings
inner: Completely Bounded Multilinear Mappings

dominate

The spaces | Examples | Examples

dual

of an operator space: see operator space
operator space tensor norm: see operator space tensor norm
operator space tensor product: see operator space tensor product

embedding

canonical: The dual | Completely integral mappings

examples

Examples |

Haagerup tensor product

Some formulae for the

hilbertian operator spaces

The spaces

injective op. space tensor product

Some formulae for the

module Haagerup tensor product

Examples

of operator modules

Basic examples of operator

operator algebra

Operator algebras | Examples

operator space

Examples | Matrices over an operator

operator spaces

completely locally reflexive: Examples

projective op. space tensor product

Some formulae for the

extension theorem

for completely bounded module homomorphisms: Basic examples of operator
for completely bounded multilinear mappings: Completely Bounded Multilinear Mappings

factorization

through a column Hilbert space: see hilbertian operator space

finite dimensional mappings

Mapping Spaces

Grothendieck

$\H$ -tensor product: The Haagerup tensor product

$\H$ -tensor product

The Haagerup tensor product

Haagerup tensor

norm

infimum formula: The Haagerup tensor product
minimum formula: Some formulae for the
sum formula: Some formulae for the
supremum formula: Some formulae for the

product

$\H$ -tensor product: The Haagerup tensor product
interpolation: The Haagerup tensor product
involving column Hilbert space: Some formulae for the | Some formulae for the
involving row Hilbert space: Some formulae for the | Some formulae for the
lemma of Blecher and Paulsen: Some formulae for the
shuffle map: Some formulae for the | Some formulae for the
tensor matrix product $\odot_h$: Some formulae for the

hilbertian operator space