Hilbert C*-modules as a subcategory of operator systems and injectivity

被引：0

作者：

Asadi, Mohammad B. ^{[1
,2
]}

Behmani, Reza ^{[3
]}

Medghalchi, Ali R. ^{[3
]}

Nikpey, Hamed ^{[4
]}

机构：

[1] Univ Tehran, Sch Math Stat & Comp Sci, Coll Sci, Tehran, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[3] Kharazmi Univ, Dept Math, 50 Taleghani Ave, Tehran 15618, Iran

[4] Shahid Rajaee Teacher Training Univ, Dept Math, Tehran 16785136, Iran

来源：

POSITIVITY | 2018年 / 22卷 / 02期

关键词：

Hilbert C*-modules; Extension theorems; Injective objects; Completely positive maps; Completely semi-f-maps; STINESPRINGS THEOREM; MAPS;

D O I：

10.1007/s11117-017-0530-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study a category whose objects are Hilbert -modules and whose morphisms are completely semi--maps. We give a characterization of injective objects in this category. In fact, we investigate extendability of completely semi--maps on Hilbert -modules, leading to an analog of the Arveson's extension theorem for completely semi--maps (in contrast with -maps). This theorem together with previous results suggest that the completely semi--maps are proper generalizations of the completely positive maps.

引用

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页码：597 / 607

页数：11

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