本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i...本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).其中1≤p,q,r<∞且1/r=1/p+1/q.同时我们还给出了一些与log-次优化相关的不等式.展开更多
In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to inv...In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.展开更多
For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui ...For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui et al. In this paper, we discuss the relatioa between the James and the generalized yon Neumann-Jordan constants, and establish an inequality between them： C（P）NJ（X） ≤ J（X） with p 〉 2, which covers the well-known inequality CNJ（X） ≤ J（X）. We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.展开更多
文摘本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).其中1≤p,q,r<∞且1/r=1/p+1/q.同时我们还给出了一些与log-次优化相关的不等式.
基金supported by the Daejin University grants in 2010
文摘In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11271112 and 11201127)Innovation Scientists and Technicians Troop Construction Projects of He’nan Province(Grant No.114200510011,C20150027)
文摘For a non-trivial Banach space X, let J（X）,CNj（X）,C（P）NJ（X） respectively stand for the James constant, the yon Neumann-Jordan constant and the generalized yon Neumann-Jordan constant receatly inroduced by Cui et al. In this paper, we discuss the relatioa between the James and the generalized yon Neumann-Jordan constants, and establish an inequality between them： C（P）NJ（X） ≤ J（X） with p 〉 2, which covers the well-known inequality CNJ（X） ≤ J（X）. We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.
