Interpolation of bilinear operators and compactness

@article{Silva2010InterpolationOB,
  title={Interpolation of bilinear operators and compactness},
  author={Eduardo Brandani da Silva and Dicesar Lass Fernandez},
  journal={arXiv: Functional Analysis},
  year={2010}
}
The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method. 
Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces
TLDR
Working in the setting of quasi-Banach couples, a formula is established for the measure of non-compactness of bilinear operators interpolated by the general real method.
Interpolation of compact bilinear operators
We investigate the stability of compactness of bilinear operators acting on the product of interpolation of Banach spaces. We develop a general framework for such results and our method applies to
Interpolation of compact bilinear operators among quasi-Banach spaces and applications
We study the interpolation properties of compact bilinear operators by the general real method among quasi‐Banach couples. As an application we show that commutators of Calderon–Zygmund bilinear
On interpolation properties of compact bilinear operators
We investigate interpolation properties of compact bilinear operators under the general real method. Results apply in particular to the real method with a function parameter and also to the complex
On the interpolation of the measure of non-compactness of bilinear operators with weak assumptions on the boundedness of the operator
Abstract We complete the range of the parameters in the interpolation formula established by Mastylo and Silva for the measure of non-compactness of a bilinear operator interpolated by the real
A compactness result of Janson type for bilinear operators
We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.
The Australian Journal of Mathematical Analysis and Applications
Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators
Interpolation of Holomorphic functions
Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map f : X0 +X1 → Y0 +Y1 to the
Real Interpolation of Compact Bilinear Operators
We establish an analog for bilinear operators of the compactness interpolation result for bounded linear operators proved by Cwikel and Cobos, Kühn and Schonbek. We work with the assumption that
Compact Bilinear Operators and Commutators
First published in Proceedings of the American Mathematical Society, volume 141, published by the American Mathematical Society. Also available electronically from
...
1
2
...

References

SHOWING 1-10 OF 18 REFERENCES
Interpolation of some spaces of Orlicz type I
A result on interpolation of bilinear operators on A f,F spaces is proved. The corresponding results of Lions and Peetre as well as Zafran turn out to be particular cases of the one given here.
On interpolation of bilinear operators
Abstract In this paper we study interpolation of bilinear operators between products of Banach spaces generated by abstract methods of interpolation in the sense of Aronszajn and Gagliardo. A variant
On ψ- interpolation spaces
In this paper the sequence Banach space ψ (Z) is defined for a class of convex functions ψ , and properties of the Kand Jinterpolation spaces (E0,E1)θ ,ψ,K and (E0,E1)θ ,ψ,J for a Banach couple E =
Interpolation of compactness using Aronszajn-Gagliardo functors
AbstractWe prove that ifT: A0 →B0 andT: A1 →B1 both are compact, then $$T:F(\bar A) \to F(\bar B)$$ is also compact, whereF is the minimal or the maximal functor in the sense of Aronszajn-Gagliardo.
Interpolation Spaces: An Introduction
1. Some Classical Theorems.- 1.1. The Riesz-Thorin Theorem.- 1.2. Applications of the Riesz-Thorin Theorem.- 1.3. The Marcinkiewicz Theorem.- 1.4. An Application of the Marcinkiewicz Theorem.- 1.5.
Interpolation of Orlicz spaces
On interpolation of multi-linear operators
On interpolation of multilinear operators , Function spaces and applications
  • Proc . US - Swed . Semin . , Lund / Swed . , Lect . Notes Math .
  • 1988
...
1
2
...