搜狗做题网巴拿赫代数求逆,有正确回答追加50-100分
来源：学生作业帮 编辑：搜狗做题网作业帮 分类：英语作业 时间：2024/05/14 04:45:44
巴拿赫代数求逆,有正确回答追加50-100分
A是个unital Banach algebra,大概叫单位性巴拿赫代数吧.1是单位,a,b在A当中,已知1-ab的逆是c,求证1-ba的逆是1+bca.再证Spectrum （ab） U {0}=Spectrum (ba) U {0}.最后求证不存在a跟b使得ab-ba=1.
主要是第一问,做出来我再补悬赏,50-100分
没学过的自然看不懂……原题是这个：
Let A be a unital Banach algebra with unit 1A. Prove that, for elements a and
b in A, the element, if the element 1A − ab is invertible with inverse c then the
element 1A −ba is invertible with inverse 1A +bca. Deduce that, for all elements a
and b in A,
σA(ab) ∪ {0} = σA(ba) ∪ {0}.
Hence, or otherwise, show that there are no elements a and b in A for which
ab − ba = 1A.
A是个unital Banach algebra,大概叫单位性巴拿赫代数吧.1是单位,a,b在A当中,已知1-ab的逆是c,求证1-ba的逆是1+bca.再证Spectrum （ab） U {0}=Spectrum (ba) U {0}.最后求证不存在a跟b使得ab-ba=1.
主要是第一问,做出来我再补悬赏,50-100分
没学过的自然看不懂……原题是这个：
Let A be a unital Banach algebra with unit 1A. Prove that, for elements a and
b in A, the element, if the element 1A − ab is invertible with inverse c then the
element 1A −ba is invertible with inverse 1A +bca. Deduce that, for all elements a
and b in A,
σA(ab) ∪ {0} = σA(ba) ∪ {0}.
Hence, or otherwise, show that there are no elements a and b in A for which
ab − ba = 1A.
(1-ab)c=1
c-abc=1
abc=c-1
(1-ba)(1+bca)
=1-ba+bca-babca
=1-ba+bca-b(c-1)a
=1-ba+bca-bca+ba
=1
c-abc=1
abc=c-1
(1-ba)(1+bca)
=1-ba+bca-babca
=1-ba+bca-b(c-1)a
=1-ba+bca-bca+ba
=1