An Elementary Proof for a Characterization of *-isomorphisms
نویسندگان
چکیده
We give an elementary proof of a result which characterizes onto *-isomorphisms of the algebra BL(H) of all the bounded linear operators on a Hilbert space H. A known proof of this result (Arveson, 1976) relies on the theory of irreducible representations of C∗-algebras, whereas the proof given by us is based on elementary properties of operators on a Hilbert space which can be found in any introductory text on Functional Analysis.
منابع مشابه
A Linear Logical View of Linear Type Isomorphisms
The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years. Isomorphisms in weak system (like linear lambda calculus) have recently been investigated due to their practical interest in library search. In this paper we give a remarkably simple and elegant characterization of linear iso...
متن کاملA linear logical view of linear type
The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years. Isomorphisms in weak system (like linear lambda calculus) have recently been investigated due to their practical interest in library search. In this paper we give a remarkably simple and elegant characterization of linear iso...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملConnected Simple Systems and the Conley Functor
The Conley index is a topological tool used in the qualitative theory of differential equations and dynamical systems (see [1], [10], [4]). In the simplest setting it takes the form of an object of a certain category (homotopy category of metric spaces, category of graded moduli etc.), which is known up to an isomorphism. This lack of precision is caused by the fact that there are many so calle...
متن کاملSUBSPACES OF c 0 ( N ) AND LIPSCHITZ ISOMORPHISMS
We show that the class of subspaces of c0(N) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to c0(N) is linearly isomorphic to c0(N). The proof relies in part on an isomorphic characterization of subspaces of c0(N) as separable spaces having an equivalent norm such that the weak-star and norm topologies quantitatively agree on t...
متن کامل