Topics in Banach space theory

By Fernando Albiac, Nigel J. Kalton. 2006

1,137 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/55021c79cba58d09317d038b8b5d62d100954113

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Citations in the corpus

γ-Radonifying Operators: A Survey (2010, neutral): “6(1) can be given for Banach spaces E having type p ∈ [1, 2].”
Kato's square root problem in Banach spaces (2007, background): “A gentle introduction to this topic can be found in [1].”
On the dual positive Schur property in Banach lattices (2013, background): “If λ is the Lebesgue measure on the unit interval, p, q ∈ (1,∞) {2} are distinct, then L(λ) generated by ψ(r, t) = r 1[0, 2 ](t) + r 1[ 2 ,1](t) is isomorphic (as a Banach space) to none Orlicz space (see [14] for details).”
Isomorphic copies in the lattice E and its symmetrization E(∗) with applications to Orlicz–Lorentz spaces (2009, result): “In particular, the notions related to Schauder bases, basic sequences or related to the theory of lattices are analogous to the corresponding notions in Banach spaces or Banach lattices which can be found in [2,3,5,25,27,28,41].”
Greedy approximation for biorthogonal systems in quasi-Banach spaces (2019, methodology): “Through this paper we use standard facts and notation from Banach spaces and approximation theory (see [14]).”
The non-linear geometry of Banach spaces after Nigel Kalton (2012, neutral): “From the recent textbooks that may be used in the area we mention [4] and [29].”
The free Banach lattice generated by a Banach space (2017, background): “ By considering the natural inclusion of L∞ = L∗ 1 in L1, each fn can be seen as an element of H[L1]+. In fact, we have fn ∈ FBL[L1]+ and kfnkFBL[L 1] = 1, because fn = X2n j=1 |δχI n,j | and 1 = fn(χ[0,1]) ≤ kfnk∞ ≤ kfnkFBL[L 1] ≤ X2n j=1 kδχI n,j kFBL[L 1] = X2n j=1 kχIn,j k1 = 1. Fix any g ∈ FBL[”
Rectifiable and flat G chains in a metric space (2012, methodology): “To see that the two norms are M̂ and M are actually comparable, we use the following corollary of John’s theorem [2]: LEMMA 5.”