منابع مشابه
A proof of the Russo–Dye theorem for JB∗-algebras
We give a new and clever proof of the Russo–Dye theorem for JB∗-algebras, which depends on certain recent tools due to the present author. The proof given here is quite different from the known proof by J. D. M. Wright and M. A. Youngson. The approach adapted here is motivated by the corresponding C∗-algebra results due to L. T. Gardner, R. V. Kadison and G. K. Pedersen. Accordingly, it yields ...
متن کاملAbsolutely Continuous Representations and a Kaplansky Density Theorem for Free Semigroup Algebras
We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a ∗-extendible representation σ. A ∗-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known exa...
متن کاملKaplansky Theorem for Completely Regular Spaces
Let X,Y be realcompact spaces or completely regular spaces consisting of Gδ-points. Let φ be a linear bijective map from C(X) (resp. C(X)) onto C(Y ) (resp. C(Y )). We show that if φ preserves nonvanishing functions, that is, f(x) 6= 0,∀x ∈ X, ⇐⇒ φ(f)(y) 6= 0,∀ y ∈ Y, then φ is a weighted composition operator φ(f) = φ(1) · f ◦ τ, arising from a homeomorphism τ : Y → X. This result is applied al...
متن کاملCHEBYSHEV SUBALGEBRAS OF JB-ALGEBRAS
In this note, we characterize Chebyshev subalgebras of unital JB-algebras. We exhibit that if B is Chebyshev subalgebra of a unital JB-algebra A, then either B is a trivial subalgebra of A or A= H R .l, where H is a Hilbert space
متن کاملGeometric Unitaries in Jb-algebras
In this article, we study geometric unitaries of JB-algebras (in particular, self-adjoint parts of C∗-algebras). We will show that the geometric unitaries of a JB algebra are precisely those central algebraic unitaries (or central symmetries). We will also show that the group of surjective isometries on a JB-algebra A (with point-norm topology) is the semi-direct product of the canonical action...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1998
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181071749