Star order on operator and function algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00182390" target="_blank" >RIV/68407700:21230/11:00182390 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.5486/PMD.2011.5006" target="_blank" >http://dx.doi.org/10.5486/PMD.2011.5006</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5486/PMD.2011.5006" target="_blank" >10.5486/PMD.2011.5006</a>

Result language
angličtina
Original language name
Star order on operator and function algebras
Original language description
The paper deals with the star order on proper *-algebras. Many results on the star order on matrix algebras and algebras of bounded operators acting on a Hilbert space are generalized to the C*-algebraic context. We characterize the star order on partialisometries in proper *-algebras in terms of their initial and final projections. As a corollary, we present a new characterization of infinite C*-algebras. Further, main results concern the infimum and supremum problem for the star order on a C*-algebraC(X) of all continuous complex-valued functions on a Hausdorff topological space X. We show that if X is locally connected or hyperstonean, then any upper bounded set in C(X) has an infimum and a supremum in the star order.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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