We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-...We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-1）） is a r-null set of H, where NG（f-1） is the set of all the points of Gateaux non-diiTerentiability of f -1.展开更多
文摘本文研究Hilbert空间H上投影算子组的联合谱.首先通过计算给出正则投影对的联合谱,进而给出一般的投影算子对的联合谱.本文还对两个投影算子的和与差的可逆性给出一些等价刻画.特别地,当P和Q为正则投影对时,本文通过计算算子组[I, P, Q]的联合谱来给出σ(P+Q)和σ(P-Q)的具体刻画.反过来,本文证明两类具有特定形式的复数集分别是Hilbert空间上正则投影对的和与差的谱.本文也给出一般的投影算子对的和与差的谱.最后,本文计算特定条件下的3个投影算子组[P, Q, R]的联合谱.
基金supported by the National Natural Science Foundation of China(11171066)the Natural Science Foundation of Fujian Province(2013J01003)
文摘We prove that for every Lipschitz isomorphism f from a separable Hilbert space H to a Banach space Y with Radon-Nikodym property, there is a bounded surjective linear operator T： H → Y so that （f ＋ T）-1 （NG（f-1）） is a r-null set of H, where NG（f-1） is the set of all the points of Gateaux non-diiTerentiability of f -1.
