Page 1

Displaying 1 – 13 of 13

Showing per page

Ultrasymmetric sequence spaces in approximation theory.

Evgeniy Pustylnik (2006)

Collectanea Mathematica

Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {an*} mean the decreasing rearrangement of a sequence {|an|}. A sequence space lφ,E with symmetric (quasi)norm || {φ(n)an*} ||Ê is called ultrasymmetric, because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λφ and Mφ. We study properties of the spaces lφ,E for all admissible...

Uniqueness of minimal projections onto two-dimensional subspaces

Boris Shekhtman, Lesław Skrzypek (2005)

Studia Mathematica

We prove that minimal projections from L p (1 < p < ∞) onto any two-dimensional subspace are unique. This result complements the theorems of W. Odyniec ([OL, Theorem I.1.3], [O3]). We also investigate the minimal number of norming points for such projections.

Upper and lower estimates for Schauder frames and atomic decompositions

Kevin Beanland, Daniel Freeman, Rui Liu (2015)

Fundamenta Mathematicae

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite-dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable...

Currently displaying 1 – 13 of 13

Page 1