Covariant representations on Krein<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:math>-modules associated to pairs of two maps

Heo, Jaeseong; Ji, Un Cig; Kim, Young Yi

doi:10.1016/j.jmaa.2012.08.027

Cited by 5 publications

(4 citation statements)

References 9 publications

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“…We also establish a covariant version of the KSGNS type theorem for a covariant α-completely positive map and study the structure of minimal covariant KSGNS constructions. Our result provide some variants and some generalizations of results of [15] in the context of maps on Krein C * -modules.…”

Section: Definition 12 Letmentioning

confidence: 57%

“…Since then many mathematicians have investigated them. Recently Heo et al [12,15] studied Krein C * -modules and covariant representations on Krein C * -modules. A treatment of operator convex functions is presented in [22].…”

Section: 2mentioning

confidence: 99%

“…Moreover, if (π ϕ , V Φ , v t , (K 1 , J 3 )) is the minimal KSGNS construction associated to ϕ, then ( π ϕ , V Φ , (K 1 , J 3 )) is the minimal KSGNS construction associated to ϕ, where π ϕ (f ) = G π ϕ (f (t)) v t dt for all f ∈ C c (G, A). The next result may be compared with [15,Corollary 4.3].…”

Section: Covariant α-Cp Mapsmentioning

confidence: 99%

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KSGNS Type Constructions for $$\alpha $$ α -Completely Positive Maps on Krein $$C^*$$ C ∗ -Modules

Moslehian

Joiţa

2015

Complex Anal. Oper. Theory

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In this paper, we investigate Φ-maps associated to a certain type of αcompletely positive maps. We then prove a KSGNS (Kasparov-Stinespring-Gel'fand-Naimark-Segal) type theorem for α-completely positive maps on Krein C * -modules and show that the minimal KSGNS construction is unique up to unitary equivalence. We also establish a covariant version of the KSGNS type theorem for a covariant α-completely positive map and study the structure of minimal covariant KSGNS constructions.1991 Mathematics Subject Classification. Primary 46L08; Secondary 47B50, 46L05.

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Section: Definition 12 Letmentioning

confidence: 57%

Section: 2mentioning

confidence: 99%

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KSGNS Type Constructions for $$\alpha $$ α -Completely Positive Maps on Krein $$C^*$$ C ∗ -Modules

Moslehian

Joiţa

2015

Complex Anal. Oper. Theory

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“…From the motivation in local quantum field theory, we introduced the notion of α-completely positive (α-CP) maps between (locally) C * -algebras, which generalizes α-positivity [15] and P -functionals [17]. The α-complete positivity was studied in several papers [8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

BURES DISTANCE FOR $\alpha$-COMPLETELY POSITIVE MAPS AND TRANSITION PROBABILITY BETWEEN $P$-FUNCTIONALS

Heo¹

2015

Taiwanese J. Math.

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In this paper we discuss the Bures distance between α-CP maps on a C * -algebra and the transition probability between P -functionals on a *-algebra. We first review the notion of α-CP maps and the representation theorem associated to α-CP maps. Using the Krein space representation and the set of intertwiners between Krein space representations, we study the Bures distance between α-CP maps. We prove that the transition probability between P -functionals can be estimated by some functionals using J-representations on Krein spaces.

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A Radon–Nikodým type theorem for invariant symmetric completely positive and completely bounded multilinear maps on Hilbert C*-modules

Heo

Joia

2019

Linear and Multilinear Algebra

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Covariant representations on KreinC∗-modules associated to pairs of two maps

Cited by 5 publications

References 9 publications

KSGNS Type Constructions for $$\alpha $$ α -Completely Positive Maps on Krein $$C^*$$ C ∗ -Modules

KSGNS Type Constructions for $$\alpha $$ α -Completely Positive Maps on Krein $$C^*$$ C ∗ -Modules

BURES DISTANCE FOR $\alpha$-COMPLETELY POSITIVE MAPS AND TRANSITION PROBABILITY BETWEEN $P$-FUNCTIONALS

A Radon–Nikodým type theorem for invariant symmetric completely positive and completely bounded multilinear maps on Hilbert C*-modules

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