Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFactorization of the identity through operators with large diagonal
56
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 Banach space, there exists an operator for which the answer to the question is negative. By contrast, for any operator on the mixed-norm Hardy spaces $H^p(H^q)$, where $1 leq p,q < infty$, with the bi-parameter Haar system, this problem always has a positive solution. The spaces $L^p, 1 < p < infty$, were treated first by Andrew~[{em Studia Math.}~1979].
rate research
Read More
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 $A$.
In this paper we give exact values of the best $n$-term approximation widths of diagonal operators between $ell_p(mathbb{N})$ and $ell_q(mathbb{N})$ with $0<p,qleq infty$. The result will be applied to obtain the asymptotic constants of best $n$-term approximation widths of embeddings of function spaces with mixed smoothness by trigonometric system.
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$ extension theorem by Whitney to Banach spaces.
A full description of the membership in the Schatten ideal $S_ p(A^2_{omega})$ for $0<p<infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.
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 $ell^infty$-sum, and let $T:Zto Z$ be a bounded linear operator, with a large diagonal, i.e. $$inf_{k,j} big|e^*_{(k,j)}(T(e_{(k,j)})big|>0.$$ Under which condition does the identity on $Z$ factor through $T$? The purpose of this paper is to formulate general conditions for which the answer is positive.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
