ON THE JOINT SPECTRUM FOR N-TUPLE OF HYPONORMAL OPERATORS

摘要

＜正＞ Let A=（A1,…,A,）be an n-tuple of double commuting hyponormal operators.It is-proved that:1.The joint spectrum of A has a Cartesian decomposition:Re[Sp（A）]=Sp（ReA）,Im[Sp（A）]=Sp（ImA）;2.The.joint resolvent of A satisfies the growth condition:‖（）‖=1/（dist（z,Sp（A）））;3.If 0σ（Ai）,i=1,2,…,n,then‖A‖=γsp（A）.