Continuous factorization of the identity matrix

Abstract

We investigate conditions under which the identity matrix $I_n$ can be continuously factorized through a continuous $N\times N$ matrix function $A$ with domain in $\mathbb{R}$. We study the relationship of the dimension $N$, the diagonal entries of $A$, and the norm of $A$ to the dimension $n$ and the norms of the matrices that witness the factorization of $I_n$ through $A$.

arXiv comment14 pages

References in corpus (7)

• Factorization of the identity through operators with large diagonal
• Subsymmetric weak${}^{\ast }$ Schauder bases and factorization of the identity
• Factorization in mixed norm Hardy and BMO spaces
• Factorization in $S{L}^{\infty }$
• Dimension dependence of factorization problems: Hardy spaces and $S{L}_n^{\infty }$
• Dimension dependence of factorization problems: bi-parameter Hardy spaces
• Direct sums of finite dimensional $S{L}_n^{\infty }$ spaces