A new approach to Hilbert $C^*$-modules

DOI10.1007/s002080050033zbMath0874.46037OpenAlexW2018958639MaRDI QIDQ1359528

Publication date: 14 August 1997

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050033

zbMATH Keywords

$C^*$-module Eilenberg-Watts theorem Haagerup tensor norm completely bounded norm categorical $C^*$-module fundamental Morita theorem HOM-tensor relations interior tensor product isomorphism of $C^*$-module categories operator space structure strong Morita equivalence of $C^*$-algebras

Mathematics Subject Classification ID

Generalizations of inner products (semi-inner products, partial inner products, etc.) (46C50) Abstract operator algebras on Hilbert spaces (47L30) General theory of (C^*)-algebras (46L05) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Categories, functors in functional analysis (46M15) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Linear spaces of operators (47L05) Tensor products in functional analysis (46M05)

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A new approach to Hilbert \(C^*\)-modules