On the uniform approximation property in Banach spaces

1984 ◽  
Vol 49 (4) ◽  
pp. 343-359 ◽  
Author(s):  
A. Szankowski
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

scholarly journals On the duality of the uniform approximation property in Banach spaces

1991 ◽  
Vol 35 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Vania Mascioni
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

scholarly journals Some remarks on the uniform approximation property in Banach spaces

1990 ◽  
Vol 96 (3) ◽  
pp. 243-253 ◽  
Author(s):  
Vania Mascioni
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

scholarly journals Homological characterizations of the approximation property for Banach spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Yu. V. Selivanov
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Cohomology Group ◽  
Approximation Property ◽  
Three Dimensional ◽  
Nuclear Operators ◽  
Finite Dimensionality

Let E be a Banach space, and let N(E) be the Banach algebra of all nuclear operators on E. In this work, we shall study the homological properties of this algebra. Some of these properties turn out to be equivalent to the (Grothendieck) approximation property for E. These include:(i) biprojectivity of N(E);(ii) biflatness of N(E);(iii) homological finite-dimensionality of N(E);(iv) vanishing of the three-dimensional cohomology group, H3(N(E), N(E)).

scholarly journals THE QUOTIENT ALGEBRA OF COMPACT-BY-APPROXIMABLE OPERATORS ON BANACH SPACES FAILING THE APPROXIMATION PROPERTY

2019 ◽  
pp. 1-23
Author(s):  
HANS-OLAV TYLLI ◽  
HENRIK WIRZENIUS
Keyword(s):  
Banach Spaces ◽  
Structural Properties ◽  
Approximation Property ◽  
Quotient Algebra ◽  
Isomorphic Embedding ◽  
Compact Approximation

We initiate a study of structural properties of the quotient algebra ${\mathcal{K}}(X)/{\mathcal{A}}(X)$ of the compact-by-approximable operators on Banach spaces $X$ failing the approximation property. Our main results and examples include the following: (i) there is a linear isomorphic embedding from $c_{0}$ into ${\mathcal{K}}(Z)/{\mathcal{A}}(Z)$ , where $Z$ belongs to the class of Banach spaces constructed by Willis that have the metric compact approximation property but fail the approximation property, (ii) there is a linear isomorphic embedding from a nonseparable space $c_{0}(\unicode[STIX]{x1D6E4})$ into ${\mathcal{K}}(Z_{FJ})/{\mathcal{A}}(Z_{FJ})$ , where $Z_{FJ}$ is a universal compact factorisation space arising from the work of Johnson and Figiel.

ON ENFLO'S METHOD OF CONSTRUCTING BANACH SPACES WITHOUT THE APPROXIMATION PROPERTY

1974 ◽  
Vol 29 (6) ◽  
pp. 157-170
Author(s):  
T Figiel ◽  
A Pełczyński
Keyword(s):  
Banach Spaces ◽  
Approximation Property

scholarly journals On the bounded approximation property in Banach spaces

2013 ◽  
Vol 198 (1) ◽  
pp. 243-259 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Yolanda Moreno
Keyword(s):  
Banach Spaces ◽  
Approximation Property

scholarly journals Banach spaces of homogeneous polynomials without the approximation property

2015 ◽  
Vol 65 (2) ◽  
pp. 367-374 ◽  
Author(s):  
Seán Dineen ◽  
Jorge Mujica
Keyword(s):  
Banach Spaces ◽  
Approximation Property ◽  
Homogeneous Polynomials
Sign in / Sign up

Export Citation Format

Share Document