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## Studia Mathematica

1999 | 136 | 1 | 37-47
Tytuł artykułu

### Supporting sequences of pure states on JB algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that any sequence $(φ_n)$ of mutually orthogonal pure states on a JB algebra A such that $(φ_n)$ forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence $(a_n)$ consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for $(φ_n)$ in the sense of $φ_n(a_n)=1$ for all n. Moreover, if A is separable then $(a_n)$ can be taken such that $(φ_n)$ is uniquely determined by the biorthogonality condition $φ_n(a_n)=1$. Consequences of this result improving hitherto known extension theorems for C*-algebras and descriptions of dual JB algebras are given.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
37-47
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-07-20
poprawiono
1999-02-18
Twórcy
autor
• Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27 Praha 6, Czech Republic
Bibliografia
• [1] J. F. Aarnes and R. V. Kadison, Pure states and approximate identities, Proc. Amer. Math. Soc. 21 (1969), 749-752.
• [2] C. A. Akemann, Approximate units and maximal abelian C* -subalgebras, Pacific J. Math. 33 (1970), 543-550.
• [3] C. A. Akemann, Left ideal structure of C* -algebras, J. Funct. Anal. 6 (1970), 305-317.
• [4] C. A. Akemann, J. Anderson and G. K. Pedersen, Excising states on C* -algebras, Canad. J. Math. 38 (1986), 1239-1260.
• [5] C. A. Akemann, J. Anderson and G. K. Pedersen, Approaching infinity in C* -algebras, J. Operator Theory 21 (1989), 255-271.
• [6] J. Anderson, Extensions, restrictions, and representations of states on C* - algebras, Trans. Amer. Math. Soc. 249 (1979), 303-329.
• [7] L. J. Bunce, The theory and structure of dual JB-algebras, Math. Z. 180 (1982), 525-534.
• [8] S. P. Gudder, Stochastic Methods in Quantum Mechanics, North-Holland, Amsterdam, 1979.
• [9] J. Hamhalter, Gleason property and extensions of states on projection logics, Bull. London Math. Soc. 26 (1994), 367-372.
• [10] J. Hamhalter, Determinacy of states and independence of operator algebras, Internat. J. Theoret. Phys. 37 (1998), 599-607.
• [11] H. Hanche-Olsen and E. Størmer, Jordan Operator Algebras, Pitman, Boston, 1984.
• [12] R. V. Kadison and I. M. Singer, Extensions of pure states, Amer. J. Math. 81 (1959), 383-400.
• [13] I. E. Segal, Postulates for general quantum mechanics, Ann. of Math. 48 (1947), 930-938.
• [14] E. Størmer, Irreducible Jordan algebras of self-adjoint operators, Trans. Amer. Math. Soc. 130 (1968), 153-166.
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Bibliografia
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