pro-C-star-algebra

A **pro-C-star-algebra** (also called locally C-star algebra) is very much like a pro-object in the category of C-star-algebras, but the inverse limits are in fact taken in an ambient category of topological *-algebras. $\sigma$-$C^*$-algebras are those pro-$C^*$-algebras which may be obtained as countable inverse limits (there are also intrinsic characterizations in terms of seminorms).

- N. C. Phillips,
*Inverse limits of $C^\ast$-algebras*, J. Operator Theory 19 (1988) 159–195, pdf;*Inverse limits of $C^\ast$-algebras*, in: Operator Algebras and Applications vol. 1, Structure Theory K-theory, Geometry and Topology (London Math. Soc. Lecture Note Series), D. E. Evans, M. Takesaki, eds.;*Representable K-theory for $\sigma$-$C^*$-algebras*, K-Theory**3**, 441–478 (1989) - Massoud Amini,
*Locally compact pro-$C^\ast$-algebras*, math.OA/0205253 - Maria Joița,
*Hilbert modules over locally $C^*$-algebras*, thesis, Editura Universitatii Bucuresti 2006 pdf;*Crossed products of locally $C^*$-algebras*, Rocky Mountain J. Math.**37**:5 (2007) 1623-1644 jstor;*A new look at the crossed products of pro-$C^*$-algebras*; Annals of Functional Analysis, 2015;*On representations associated with completely n-positive linear maps on pro-$C^*$-algebras*, Chinese Annals of Mathematics, Series B, 2008;*Pro-$C^*$-algebras associated to tensor products of pro-$C^*$-correspondences*, J. Math. Anal. Appl.**455**: 2 (2017) 1822-1834 doi; Crossed Products of pro-$C^*$-algebras and Hilbert pro-$C^*$-modules_, M. Bull. Malays. Math. Sci. Soc. (2015) 38:1053 doi - Maria Joiţa, Ioannis Zarakas,
*Crossed products by Hilbert pro-$C^*$-bimodules*, Studia Mathematica 215 (2013), 139-156 doi;*A construction of pro-$C^*$-algebras from pro-$C^*$-correspondences*, J. Operator Theory**74**:1 (2015) 195-211, doi - Rachid El Harti, N. Christopher Phillips, Paulo R. Pinto,
*Profinite pro-$C^\ast$-algebras and pro-$C^\ast$-algebras of profinite groups*, arxiv/1110.3411 - Snigdhayan Mahanta,
*Noncommutative correspondence categories, simplicial sets and pro-$C^\ast$-algebras*, arxiv/0906.5400 - Ilan Barnea, Michael Joachimand Snigdhayan Mahanta,
*Model structure on projective systems of $C^*$-algebras and bivariant homology theories*, New York J. Math.**23**(2017) 383–439 pdf *Atiyah-Jänich Theorem for σ-C**-algebras_ 2017, Applied Categorical Structures***25**:5 (2017) 893–905 doi

There is a functor $(-)_b:pro-C^\ast\to C^\ast$ which is the dual of Stone-Čech compactification:

- Rachid El Harti, Gábor Lukács,
*Bounded and unitary elements in pro-$C^\ast$-algebras*, Applied Categorical Structures**14**:2, 2006, 151–164 doi math.CT/0511068

A class of topological algebras which correspond to pro-$C^\ast$-algebras can be characterized in terms of properties of the topological algebra:

- S.J. Bhatt, D.J. Karia,
*An intrinsic characterization of pro-$C^\ast$-algebras and its applications*, J. Math. Anal. Appl.**175**:1 (1993) 68–80, doi

Last revised on October 24, 2019 at 10:23:04. See the history of this page for a list of all contributions to it.