$C^*$-isomorphisms, Jordan isomorphisms, and numerical range preserving maps
نویسندگان
چکیده
منابع مشابه
C∗-Isomorphisms, Jordan Isomorphisms, and Numerical Range Preserving Maps
Let V = B(H) or S(H), where B(H) is the algebra of bounded linear operator acting on the Hilbert space H, and S(H) is the set of self-adjoint operators in B(H). Denote the numerical range of A ∈ B(H) by W (A) = {(Ax, x) : x ∈ H, (x, x) = 1}. It is shown that a surjective map φ : V→ V satisfies W (AB +BA) =W (φ(A)φ(B) + φ(B)φ(A)) for all A,B ∈ V if and only if there is a unitary operator U ∈ B(H...
متن کاملIsomorphisms Preserving Invariants
Let V and W be finite dimensional real vector spaces and let G ⊂ GL(V ) and H ⊂ GL(W ) be finite subgroups. Assume for simplicity that the actions contain no reflections. Let Y and Z denote the real algebraic varieties corresponding to R[V ] and R[W ] , respectively. If V and W are quasi-isomorphic, i.e., if there is a linear isomorphism L : V → W such that L sends G-orbits to H-orbits and L se...
متن کاملIsomorphisms in unital $C^*$-algebras
It is shown that every almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...
متن کاملOn strongly Jordan zero-product preserving maps
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...
متن کاملLattice Isomorphisms and Iterates of Nonexpansive Maps
It is easy to see that the I, norm and the sup norm 11. Ilm (Ilxll, = max{Ix, I: 1 I i 5 n)) on I?’ are polyhedral. If E is a finite dimensional Banach space with a polyhedral norm 11. )I, D is a compact subset of E and f: D + D is a nonexpansive map, Weller [2] has shown that for each x E D, there again exists an integer px such that (1.1) holds. The original arguments did not give upper bound...
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: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-08807-7