scholarly journals An extension of Nachbin’s theorem to differentiable functions on Banach spaces with the approximation property

1976 ◽  
Vol 14 (1-2) ◽  
pp. 251-258 ◽  
Author(s):  
João B. Prolla ◽  
Claudia S. Guerreiro
Keyword(s):  
Banach Spaces ◽  
Approximation Property ◽  
Differentiable Functions

scholarly journals General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
Fréchet Differentiable ◽  
General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

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.

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
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