In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the G...In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).展开更多
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
For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(...For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
基金Supported by the National Natural Science Foundation of China(11942109)the Natural Science Foundation of Hunan Province in China(2022JJ30369)。
文摘In this paper,we first discuss the boundedness of certain integral operator T_(t) on the normal weight general function space F(p,μ,s)in the unit ball Bnof C^(n).As an application of this operator,we prove that the Gleason’s problem is solvable on F(p,μ,s).
基金Supported by the National Natural Science Foundation of China(11871452,12071052the Natural Science Foundation of Henan(202300410338)the Nanhu Scholar Program for Young Scholars of XYNU。
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partially supported by the NSF of China(11671314)partially supported by the NSF of China(12171251)。
文摘For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
