B(χ)的拟同构

Quasi-automorphisms on B(X)

设x是复Banach空间,且dim x≥2,B(x)是X上有界线性算子全体组成的Banach代数,(B)A,B∈B(x),定义拟积A·B=A+B-AB,则(B(x),·)是半群.本文主要考虑了B(x)上的拟积自同构,证明了B(x)上的双射φ是拟积自同构的充要条件是φ是环自同构.

Let B（X） be the algebra of all bounded linear operators on a complex Banach space 2d with dim X≥2. For A, B ∈ B（X）, we define a quasi-product by A o B = A ＋ B - AB, then （B（X）, o） is a semi-group. In this article, we consider the quasi-automorphism on B（X）. It is proved that a bijective map on B（X） is a quasi-isomorphism if and only if to is a ring isomorphism.