Some approximation properties and nuclear operators in spaces of analytical functions

  title={Some approximation properties and nuclear operators in spaces of analytical functions},
  author={Sten Kaijser and Oleg I‎. ‎Reinov},
  journal={Advances in Operator Theory},
We introduce and investigate a new notion of the approximation property AP([c]), where c = (c(n)) is an arbitrary positive real sequence, tending to infinity. Also, we study the corresponding notio ... 


The approximation property does not imply the bounded approximation property
There is a Banach space which has the approxi- mation property but fails the bounded approximation property. The space can be chosen to have separable conjugate, hence there is a nonnuclear operator
Some Remarks on Approximation Properties with Applications
We study some known approximation properties and introduce and investigate several new approximation properties, closely connected with different quasi-normed tensor products. These are the
Subspaces without the approximation property
It is proved that the Banach spacelp with 1≦p<2 contains a subspace without AP (the case 2<p≦∞ follows from the Enflo’s construction and also from the present one). The result generalizes to the
An example of an asymptotically Hilbertian space which fails the approximation property
Following Davie's example of a Banach space failing the approximation property (1973), we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation
On james’s paper “separable conjugate spaces”
For every separable Banach spaceX there is a Banach spaceY with a separable dual such thatY ⊕X* ≈Y**. There is also a separable spaceZ so thatZ**/JZ is isomorphic toX.
Introduction to Tensor Products of Banach Spaces
This volume provides a self-contained introduction to the theory of tensor products of Banach spaces. It is written for graduate students in analysis or for researchers in other fields who wish to
Banach Spaces of Analytic Functions and Absolutely Summing Operators
Preliminaries The F. and M. Riesz theorem and duals of the disc algebra Absolutely summing operators from the disc algebra Absolutely summing operators from the disc algebra into Hilbert space The
Produits Tensoriels Topologiques Et Espaces Nucleaires
© Association des collaborateurs de Nicolas Bourbaki, 1951-1954, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. implique l’accord avec les conditions