Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(...Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.展开更多
An electrostatic accelerating column was designed and fabricated by Lanzhou University for an intense DT/D-D neutron generator. In order to achieve a neutron yield of 5.0 × 10^(12)n/s, a deuteron beam of 30 mA,ac...An electrostatic accelerating column was designed and fabricated by Lanzhou University for an intense DT/D-D neutron generator. In order to achieve a neutron yield of 5.0 × 10^(12)n/s, a deuteron beam of 30 mA,accelerated to 400 kV, and transported in the electrostatic accelerating column smoothly are required. One particle-in-cell code BEAMPATH was used to simulate the beam transport, and the IONB 1.0 code was used to simulate the intense beam envelopes. Emittance growths due to space charge effect and spherical aberration were analyzed. The simulation results show that the accelerating column can transport deuteron beam of 30 mA smoothly and the requirement for the neutron generator is satisfied.展开更多
基金the French ANR project(ANR-19-CE40-0002)the Natural Science Foundation of China(12031004).
文摘Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.
基金Supported by the National Nature Science Foundation of China(Nos.11027508 and 21327801)Ministry of Sciences and Technology of China(No.2013YQ040861)Fundamental Research Funds for the Central Universities(No.lzujbky-2015-bt07)
文摘An electrostatic accelerating column was designed and fabricated by Lanzhou University for an intense DT/D-D neutron generator. In order to achieve a neutron yield of 5.0 × 10^(12)n/s, a deuteron beam of 30 mA,accelerated to 400 kV, and transported in the electrostatic accelerating column smoothly are required. One particle-in-cell code BEAMPATH was used to simulate the beam transport, and the IONB 1.0 code was used to simulate the intense beam envelopes. Emittance growths due to space charge effect and spherical aberration were analyzed. The simulation results show that the accelerating column can transport deuteron beam of 30 mA smoothly and the requirement for the neutron generator is satisfied.
