# Some approximation properties and nuclear operators in spaces of analytical functions

@article{Kaijser2019SomeAP, title={Some approximation properties and nuclear operators in spaces of analytical functions}, author={Sten Kaijser and Oleg I. Reinov}, journal={Advances in Operator Theory}, year={2019} }

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 ...

## References

SHOWING 1-10 OF 25 REFERENCES

The approximation property does not imply the bounded approximation property

- Mathematics
- 1973

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

- Mathematics
- 2016

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

- Mathematics
- 1978

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

- Mathematics
- 2000

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”

- Mathematics
- 1971

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.

Grothendieckʼs nuclear operator theorem revisited with an application to p-null sequences

- Mathematics
- 2012

Introduction to Tensor Products of Banach Spaces

- Mathematics
- 2002

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

- Mathematics
- 1977

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

- Mathematics
- 1966

© Association des collaborateurs de Nicolas Bourbaki, 1951-1954, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions…