7 papers · 1 filter
Coarse comparison of Bessel families
Nizar El Idrissi
A Bessel family is a collection of vectors of a Hilbert space whose coefficients are square summable; orthonormal bases and frames are examples. We compare two such families by ask…
Probability measure annihilating all finite-dimensional subspaces
Nizar El Idrissi, Hicham Zoubeir
We propose in this short note a prime numbers-based method for constructing probability measures on infinite-dimensional Banach spaces annihilating all finite-dimensional subspaces…
Almost sure linear independence of absolutely continuous Hilbert space-valued random vectors with respect to a special class of Hilbert space probability measures
Nizar El Idrissi, Hicham Zoubeir
This note examines the implications of randomly selecting vectors from an infinite-dimensional Hilbert space on linear independence, assuming that for all , the first vector…
Independence, infinite dimension, and operators
Nizar El Idrissi, Samir Kabbaj
In [Appl. Comput. Harmon. Anal., 46(3):664-673, 2019], O. Christensen and M. Hasannasab observed that assuming the existence of an operator sending to for all $…
Frames generated by the functional calculus and function frames of a normal operator
Nizar El Idrissi
In this article, we prove that sequences generated by the functional calculus can be equivalently written as function sequences $(f_n(T) g)_{n \in…
Intersections of translates of finite-dimensionally valued frame spaces are conditionally slice-full and almost slice-full
Nizar El Idrissi
In recent work, the topology of frame spaces has been studied via Stiefel manifolds, revealing in particular a connectedness property for intersections of t…
Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold
Nizar El Idrissi, Samir Kabbaj, Brahim Moalige
If is a Hilbert space, the non-compact Stiefel manifold consists of independent -tuples in . In this article, we contribute to the topological study of non-comp…