Numerical radius preserving operators on 𝐵(𝐻)

Abstract

Abstract. Let H be a Hubert space over C and let B(H) denote the vector space of all bounded linear operators on H.

MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS

“…Finally, we have shown that ψ is an algebra isomorphism which preserves self-adjoint elements. Thus, by [4] ψ takes the following form: ψ(A) = U AU * for all A ∈ B(H) where U is unitary.…”

“…In the last few decades, there has been a considerable interest in the problem of characterization of maps that preserves the numerical range or the numerical radius, see for instance the papers [4,12,13,15] and the references therein. Notice that, based on the aforesaid, preserving the usual numerical range W implies the preservation of the spacial numerical range V .…”

Numerical radius preserving operators on C * -algebras

“…vTa va for every a, then T is a multiple of a C Ã -isomorphism by a scalar of modulus one. In [3] we extended Lis result to arbitary dimension. The purpose of the present note is to study the problem in the setting of a general C Ã -algebra.…”

Linear Maps Preserving Numerical Radius on Nest Algebras

“…The subject is related and has applications to many different branches of pure and applied science. In [2,3], Chan proved that if A is a unital C * -algebra then a surjective numerical radius isometry of A is a Jordan isomorphism multiplied by a fixed unitary element in the center of A. This is also true for weakly continuous, surjective numerical radius isometries of atomic nest algebras [4,5,14].…”

“…For any unit vector z, we can write z = cx + dy + eu + fv + z , where z is a vector orthogonal to [x, y, u, v]. Then 1 ≥ |c| 2 + |d| 2 + |e| 2 + |f | 2 = |c| 2 + (|a| + (1 − |a|))|d| 2 …”