COMPLETENESS OF *-SYMMETRIC GELFAND-NAIMARK-SEGAL INNER PRODUCT SPACES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00196749" target="_blank" >RIV/68407700:21230/12:00196749 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/qmath/haq041" target="_blank" >http://dx.doi.org/10.1093/qmath/haq041</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/qmath/haq041" target="_blank" >10.1093/qmath/haq041</a>

Result language
angličtina
Original language name
COMPLETENESS OF *-SYMMETRIC GELFAND-NAIMARK-SEGAL INNER PRODUCT SPACES
Original language description
Every state rho on a C*-algebra A induces a *-symmetric semi-inner product (x, y)& rho(y* x) + rho(xy*) (x, y is an element of A). The main scope of the paper is to characterize those states for which the induced *-symmetric Gelfand-Naimark-Segal inner product space is complete. It is shown that this happens precisely when rho is a finite convex combination of pure states. (It is well known that the same conclusion follows if one considers the non-symmetric semi-inner product (x, y) & rho(y* x).) In sodoing, we exhibit an interesting connection between convexity properties of states, the transitivity of irreducible representations and Banach space properties of the quotients of C*-algebra s by kernels of states.
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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Project
<a href="/en/project/GA201%2F07%2F1051" target="_blank" >GA201/07/1051: Algebraic and measure-theoretic aspects of quantum structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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