A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

Bounded Rank of C ∗-algebras

We introduce a new concept of the bounded rank (with respect to a positive constant) for unital C∗-algebras as a modification of the usual real rank. We present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K > 0 there exists a separable unital C∗-algebra Z n such that every other separable unital C∗-algebr...

Spectrum Preserving Linear Maps Between Banach Algebras

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

Non-extendable isomorphisms between affine varieties

In this paper, we report several large classes of affine varieties (over an arbitrary field K of characteristic 0) with the following property: each variety in these classes has an isomorphic copy such that the corresponding isomorphism cannot be extended to an automorphism of the ambient affine space Kn. This implies, in particular, that each of these varieties has at least two inequivalent em...

Spectrally Bounded Operators on Simple C∗-algebras

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ M r(x) for all x ∈ E, where r( · ) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple C∗-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.

Non Associative Linear Algebras