LINEAR ISOMETRIES BETWEEN REAL JB*-TRIPLES AND C*-ALGEBRAS
نویسندگان
چکیده
منابع مشابه
Surjective Real-Linear Uniform Isometries Between Complex Function Algebras
In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$, where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...
متن کاملLittle Grothendieck’s theorem for real JB*-triples
We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and corresponding pre-Hilbertian semi-norm ‖.‖φ on E such that ‖T (x)‖ ≤ 4 √ 2‖T‖ ‖x‖φ for all x ∈ E, is norm dense in the set of all bounded linear operators from E toH . As a tool for the above result, we show th...
متن کاملThe Daugavet Property of C-algebras, Jb-triples, and of Their Isometric Preduals
A Banach space X is said to have the Daugavet property if every rank-one operator T : X −→ X satisfies ‖Id + T ‖ = 1 + ‖T ‖. We give geometric characterizations of this property in the settings of C-algebras, JB-triples and their isometric preduals. We also show that, in these settings, the Daugavet property passes to ultrapowers, and thus, it is equivalent to an stronger property called the un...
متن کاملIsometries Between Matrix Algebras
As an attempt to understand linear isometries between C∗-algebras without the surjectivity assumption, we study linear isometries between matrix algebras. Denote by Mm the algebra of m×m complex matrices. If k ≥ n and φ : Mn → Mk has the form X 7→ U [X ⊕ f(X)]V or X 7→ U [X t ⊕ f(X)]V for some unitary U, V ∈ Mk and contractive linear map f : Mn → Mk, then ‖φ(X)‖ = ‖X‖ for all X ∈ Mn. We prove t...
متن کاملOn the axiomatic definition of real JB∗–triples
In the last twenty years, a theory of real Jordan triples has been developed. In 1994 T. Dang and B. Russo introduced the concept of J∗B–triple. These J∗B–triples include real C∗–algebras and complex JB∗–triples. However, concerning J∗B–triples, an important problem was left open. Indeed, the question was whether the complexification of a J∗B–triple is a complex JB∗–triple in some norm extendin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2013
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/hat033