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Maria Joiţa

Publications and source records attributed to Maria Joiţa.

15 recordsLinked to original sources
arXiv2026

Injective envelopes for locally C*-algebras

We introduce the notion of admissible injective envelope for a locally C*-algebra and show that each object in the category whose objects are unital Fréchet locally C*-algebras and whose morphisms are unital admissible local completely positive maps has a unique admissible injective envelope. The concept of admissible injectivity is stronger than that of injectivity. As a consequence, we show that a unital Fréchet locally W*-algebras is injective if and only if the C*-algebras from its Arens-Michael decomposition are injective.

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arXiv2026

The R-Shilov boundary for a local operator space

To extend the notion of the injective envelope of a unital operator space to the locally convex case, Dosi (2014) first introduced the notion of the injective R-envelope for a unital operator space and then defined the injective R-envelope for a unital local operator space as the closure of the injective R-envelope for its bounded part. In this paper, we investigate the existence of the Shilov boundary ideal in this context, as defined by Arveson (1969). To do this, by following the conceptual frameworks underlying Hamana's constructions of the injective envelope and the C*-envelope, respectively, we define the notions of the injective R-envelope and the R-C*-envelope for a unital local operator space. Furthermore, we show that the injective R-envelope construction given by us coincides with the one given by Dosi (2014).

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arXiv2023

Local boundary representations for local operator systems

In this paper, we show that the local boundary representations of a local operator system in a Frechet locally C*-algebra on quantized Frechet domains introduced by Arunkumar [Local boundary representations of locally C*-algebras, J. Math. Anal. Appl. 515(2022),2,Paper No. 126416, 14pp.] are in fact local boundary representations on Hilbert spaces. Thus, the study of local boundary representations for local operator systems in Frechet locally C*-algebras on quantized Frechet domains is reduced to the study of boundary representations for operator systems.

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arXiv2022

Factorization properties for unbounded local positive maps

In this paper we present some factorization properties for unbounded local positive maps. We show that an unbounded local positive map $ϕ$ on the minimal tensor product of the locally $C^{\ast }$-algebras $\mathcal{A}$ and $C^{\ast }(\mathcal{D}_{\mathcal{E}}),$ where $\mathcal{D}_{\mathcal{E}}$ is a Fréchet quantized domain, that is dominated by $φ\otimes $id is of the forma $ψ\otimes $id, where $ψ$ is an unbounded local positive map dominated by $φ$. As an application of this result, we show that given a local positive map $φ:$ $\mathcal{A}\rightarrow $ $\mathcal{B},$ the local positive map $φ\otimes $id$_{M_{n}\left( \mathbb{C}\right) }$ is local decomposable for some $n\geq 2$ if and only if $φ$ is a local $CP$-map. Also, we show that an unbounded local $CCP$-map $ϕ$ on the minimal tensor product of the unital locally $C^{\ast }$-algebras $\mathcal{A}$ and $\mathcal{B},$ that is dominated by $φ\otimes ψ$ is of the forma $φ\otimes \widetilde{ψ}$, where $\widetilde{ψ}$ is an unbounded local $CCP$- map dominated by $ψ$, whenever $φ$ is pure.

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arXiv2022

Unbounded local completely contractive maps

We prove a local convex version of Arveson's extension theorem and of Wittstock's extension theorem. Also we prove a Stinespring type theorem for unbounded local completely contractive maps.

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arXiv2019

On the ternary domain of a completely positive map on a Hilbert C*-module

We associate to an operator valued completely positive linear map $φ$ on a $C^{\ast }$-algebra $A$ and a Hilbert $C^{\ast }$-module $X$ over $A$ a subset $X_{φ}$ of $X,$ called '\textit{ternary domain}' of $φ$ on $X,$ which is a Hilbert $C^{\ast }$-module over the multiplicative domain of $φ$ and every $φ$-map (i.e., associated quaternary map with $φ$) acts on it as a ternary map. We also provide several characterizations for this set. The ternary domain \ of $φ$ on $A\ $ is a closed two-sided $\ast $-ideal $T_{φ}$ of the multiplicative domain of $φ$. We show that $XT_{φ}=X_{φ}$ and give several characterizations of the set $X_{φ}.$ Furthermore, we establish some relationships between $X_{φ}$ and minimal Stinespring dilation triples associate to $φ$. Finally, we show that every operator valued completely positive linear map $φ$ on a $C^{\ast }$ -algebra $A$ induces a unique (in a some sense) completely positive linear map on the linking algebra of $X$ and we determine its multiplicative domain in terms of the multiplicative domain of $φ$ and the ternary domain of $φ$ on $X$.

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arXiv2018

Comparison of Completely Positive Maps on Hilbert C*-Modules

We introduce a preorder relation in the collection of all operator valued completely positive maps on a full Hilbert C*-module and characterize this relation in terms of the Stinespring construction associated to each completely positive map.

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arXiv2017

Scattered locally C*-algebras

In this paper, we introduce the notion of a scattered locally $C^{\ast }$ -algebra and we give conditions for a locally $C^{\ast }$-algebra to be scattered. Given an action $α$ of a locally compact group $G$ on a scattered locally $C^{\ast }$-algebra $A[τ_{Γ}]$, it is natural to ask under what conditions the crossed product $A[τ_{Γ}]\times_{α}G$ is also scattered. We obtain some results concerning this question.

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arXiv2015

Crossed products by Hilbert pro-C*-bimodules versus tensor products

We show that if $(X.A)$ and $(Y,B)$ are two isomorphic Hilbert pro-$C^{\ast} $-bimodules, then the crossed product $A\times_{X}\mathbb{Z}$ of $A$ by $X$ and the crossed product $B\times_{Y}\mathbb{Z}$ of $B$ by $Y$ are isomorphic as pro-$C^{\ast}$-algebras. We also prove a property of "associativity" between " $\otimes_{\min}$" and "$\times_{X}$" $\ $as well as " $\otimes_{\max}$" and "$\times_{X}$". As an application of these results we show that the crossed product of a nuclear pro-$C^{\ast}$ -algebra $A$ by a full Hilbert pro-$C^{\ast}$-bimodule $X$ is a nuclear pro-$C^{\ast}$-algebra.

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arXiv2014

Multipliers of Hilbert pro-C*-bimodules and crossed products by Hilbert pro-C*-bimodules

In this paper we introduce the notion of multiplier of a Hilbert pro-$C^{\ast }$-bimodule and we investigate the structure of the multiplier bimodule of a Hilbert pro-$C^{\ast}$-bimodule. We also investigate the relationship between the crossed product $A\times _{X}\mathbb{Z}$ of a pro-$% C^{\ast }$-algebra $A$ by a Hilbert pro-$C^{\ast }$-bimodule $X$ over $A$, the crossed product $M(A)\times _{M(X)}\mathbb{Z}$ of the multiplier algebra $M(A)$ of $A$ by the multiplier bimodule $M(X)$ of $X$ and the multiplier algebra $M(A\times _{X}\mathbb{Z})$ of $A\times _{X}\mathbb{Z}$.

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arXiv2014

A construction of pro-C*-algebras from pro-C*-correspondences

We associate a pro-C*-algebra to a pro-C*-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C*-bimodules and the construction of pro-C*-crossed products by strong bounded automorphisms.

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arXiv2013

A Radon-Nikodym type theorem for $α$-completely positive maps on groups

We show that an operator valued $α$-completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define the same α-completely positive map. Also we introduce a pre-order relation on the collection of α-completely positive maps on a group and we characterize this relation in terms of the unitary representation associated to each map.

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