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Stabilité des C * -algèbres de feuilletages

Michel Hilsum, Georges Skandalis (1983)

Annales de l'institut Fourier

Soit A la C * -algèbre, ou bien réduite ou bien maximale, associée à la variété feuilletée ( V , F ) , et K la C * -algèbre élémentaire des opérateurs compacts. Alors, si dim F 0 , on montre que A est isomorphe à A K .

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

Maria Joiţa (2009)

Open Mathematics

We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math....

Standard commuting dilations and liftings

Santanu Dey (2012)

Colloquium Mathematicae

We identify how the standard commuting dilation of the maximal commuting piece of any row contraction, especially on a finite-dimensional Hilbert space, is associated to the minimal isometric dilation of the row contraction. Using the concept of standard commuting dilation it is also shown that if liftings of row contractions are on finite-dimensional Hilbert spaces, then there are strong restrictions on properties of the liftings.

The alternative Dunford-Pettis Property in the predual of a von Neumann algebra

Miguel Martín, Antonio M. Peralta (2001)

Studia Mathematica

Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].

The C * -algebra of a Hilbert bimodule

Sergio Doplicher, Claudia Pinzari, Rita Zuccante (1998)

Bollettino dell'Unione Matematica Italiana

Un C * -modulo hilbertiano destro X su una C * -algebra A dotato di uno * -omomorfismo isometrico ϕ : A L A X viene qui considerato come un oggetto X A della C * -categoria degli A -moduli Hilbertiani destri. Come in [11], associamo ad esso una C * -algebra O X A contenente X come un « A -bimodulo hilbertiano in O X A ». Se X è pieno e proiettivo finito O X A è la C * -algebra C * X , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, C * X è canonicamente immersa...

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