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We investigate conditions under which the identity matrix $I_n$ can be continuously factorized through a continuous $Ntimes N$ 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 $A$.
Given a Banach space~$X$ with an unconditional basis, we consider the following question: does the identity on~$X$ factor through every operator on~$X$ with large diagonal relative to the unconditional basis? We show that on Gowers unconditional Bana
We prove a version of the classical Dufresne identity for matrix processes. In particular, we show that the inverse Wishart laws on the space of positive definite r x r matrices can be realized by the infinite time horizon integral of M_t times its t
In this paper we consider the following problem: Let $X_k$, be a Banach space with a normalized basis $(e_{(k,j)})_j$, whose biorthogonals are denoted by $(e_{(k,j)}^*)_j$, for $kinmathbb{N}$, let $Z=ell^infty(X_k:kinmathbb{N})$ be their $ell^infty$-
We show that every subsymmetric Schauder basis $(e_j)$ of a Banach space $X$ has the factorization property, i.e. $I_X$ factors through every bounded operator $Tcolon Xto X$ with a $delta$-large diagonal (that is $inf_j |langle Te_j, e_j^*rangle| geq
We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach