Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm...Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.展开更多
Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups...Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups in finite factors,we show thatϕor I−ϕcan be extended to a∗-isomorphism or a∗-antiisomorphism.In particular,ϕis given by a∗-(anti-)isomorphism unless M1 and M2 are finite and c=12.展开更多
基金partly supported by Natural Science Foundation of the Xinjiang Uygur Autonomous Region(2013211A001)
文摘Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M.
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN2021000529)the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No.cstc2020jcyj-msxm X0723)+2 种基金supported by Young Talent Fund of University Association for Science and Technology in Shaanxi(Grant No.20210507)supported by National Natural Science Foundation of China(Grant Nos.11871127and 11971463)supported by National Natural Science Foundation of China(Grant Nos.11971463,11871303 and 11871127)。
文摘Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups in finite factors,we show thatϕor I−ϕcan be extended to a∗-isomorphism or a∗-antiisomorphism.In particular,ϕis given by a∗-(anti-)isomorphism unless M1 and M2 are finite and c=12.
