Metrically and topologically projective ideals of Banach algebras

Nemesh, N. T.

doi:10.1134/s0001434616030251

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…We have already mentioned that passing from the relative to topological and metric projectivity we get much less projective modules. In this connection we would like to cite a rather difficult theorem, due to N.Nemesh [24] and concerning the "classical" context. Namely, Nemesh proved that for a closed left ideal, say I, in a C * -algebra the following properties are equivalent:…”

Section: Quantum Projectivity and Ideals In C * -Algebrasmentioning

confidence: 99%

Projective Quantum Modules and Projective Ideals of C*-algebras

Helemskii

2018

Operator Theory in Different Settings and Related Applications

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We introduce in non-coordinate presentation the notions of a quantum algebra and of a quantum module over such an algebra. Then we give the definition of a projective quantum module and of a free quantum module, the latter as a particular case of the notion of a free object in a rigged category. (Here we say "quantum" instead of frequently used protean adjective "operator"). After this we discuss the general connection between projectivity and freeness. Then we show that for a Banach quantum algebra A and a Banach quantum space E the Banach quantum A-module A ⊗ op E is free, where " ⊗ op " denotes the operator-projective tensor product of Banach quantum spaces. This is used in the proof of the following theorem: all closed left ideals in a separable C * -algebra, endowed with the standard quantization, are projective left quantum modules over this algebra.Bibliography: 29 titles.

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Section: Quantum Projectivity and Ideals In C * -Algebrasmentioning

confidence: 99%

Projective Quantum Modules and Projective Ideals of C*-algebras

Helemskii

2018

Operator Theory in Different Settings and Related Applications

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The Geometry of Projective, Injective, and Flat Banach Modules

Nemesh

2019

J Math Sci

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Топологически Проективные, Инъективные И Плоские Модули Гармонического Анализа

Nemesh¹

2020

Математический сборник

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В работе изучаются гомологически тривиальные модули гармонического анализа на локально компактной группе $G$. Для $L_1(G)$- и $M(G)$-модулей $C_0(G)$, $L_p(G)$ и $M(G)$ даны критерии метрической и топологической проективности, инъективности и плоскости. В большинстве случаев модули, обладающие этими свойствами, должны быть конечномерными. Библиография: 18 названий.

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Metrically and topologically projective ideals of Banach algebras

Cited by 3 publications

References 7 publications

Projective Quantum Modules and Projective Ideals of C*-algebras

Projective Quantum Modules and Projective Ideals of C*-algebras

The Geometry of Projective, Injective, and Flat Banach Modules

Топологически Проективные, Инъективные И Плоские Модули Гармонического Анализа

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