论文标题
关于第五最大投影常数的值
On the value of the fifth maximal projection constant
论文作者
论文摘要
令$λ（m）$表示在实际$ m $二维子空间上的最大绝对投影常数。由于$ m> 1 $的唯一已知值为$λ（2）= 4/3 $，因此很难确切确定这个数量。还有数值证据表明$λ（3）=（1+ \ sqrt {5}）/2 $。在本文中，依靠某些相互无偏的等法紧密框架的新结构，我们表明$λ（5）\ geq 5（11+6 \ sqrt {5}）/59 \ of 2.06919 $。该值与B. L. Chalmers获得的$λ（5）$的数值估计相吻合，从而加强了相信这是$λ（5）$的确切值。
Let $λ(m)$ denote the maximal absolute projection constant over real $m$-dimensional subspaces. This quantity is extremely hard to determine exactly, as testified by the fact that the only known value of $λ(m)$ for $m>1$ is $λ(2)=4/3$. There is also numerical evidence indicating that $λ(3)=(1+\sqrt{5})/2$. In this paper, relying on a new construction of certain mutually unbiased equiangular tight frames, we show that $λ(5)\geq 5(11+6\sqrt{5})/59 \approx 2.06919$. This value coincides with the numerical estimation of $λ(5)$ obtained by B. L. Chalmers, thus reinforcing the belief that this is the exact value of $λ(5)$.
