scholarly journals Geometry of multilinear forms on l_1

2021 ◽  
Vol 25 (1) ◽  
pp. 57-66
Author(s):  
Sung Guen Kim
Keyword(s):  
Banach Space ◽  
Linear Forms ◽  
Multilinear Forms

We characterize extreme, exposed and smooth points in the Banach space L(nE) of continuous n-linear forms on E, and in its subspace Ls(nE) of symmetric n-linear forms on E when E = l1 and E = l1m  for n,m ∈ N with n,m ≥ 2 .

scholarly journals Geometry of multilinear forms

2019 ◽  
Vol 22 (02) ◽  
pp. 1950011 ◽  
Author(s):  
W. V. Cavalcante ◽  
D. M. Pellegrino ◽  
E. V. Teixeira
Keyword(s):  
Unit Ball ◽  
Extreme Points ◽  
Linear Forms ◽  
Multilinear Forms ◽  
Elementary Steps ◽  
Full Characterization ◽  
Constructive Process

We develop a constructive process which determines all extreme points of the unit ball in the space of [Formula: see text]-linear forms, [Formula: see text] Our method provides a full characterization of the geometry of that space through finitely many elementary steps, and thus it can be extensively applied in both computational as well as theoretical problems; few consequences are also derived in this paper.

scholarly journals Norm Attaining Multilinear Forms on

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Yousef Saleh
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Bilinear Forms ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Multilinear Forms ◽  
Arbitrary Measure ◽  
Norm Attaining Operators ◽  
Norm Attaining

Given an arbitrary measure , this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on . However, we have the density if and only if is purely atomic. Furthermore, the study presents an example of a Banach space in which the set of norm attaining operators from into is dense in the space of all bounded linear operators . In contrast, the set of norm attaining bilinear forms on is not dense in the space of continuous bilinear forms on .

NEW SUFFICIENT CONDITIONS FOR THE DENSENESS OF NORM ATTAINING MULTILINEAR FORMS

2002 ◽  
Vol 34 (2) ◽  
pp. 212-218 ◽  
Author(s):  
RAFAEL PAYÁ ◽  
YOUSEF SALEH
Keyword(s):  
Banach Space ◽  
Sufficient Conditions ◽  
Symmetric Case ◽  
Multilinear Forms ◽  
Norm Attaining

This paper gives new sufficient conditions for the density of the set of norm attaining multilinear forms in the space of all continuous multilinear forms on a Banach space. The symmetric case is also discussed.

scholarly journals Weakly compact multilinear mappings

1997 ◽  
Vol 40 (1) ◽  
pp. 181-192 ◽  
Author(s):  
Richard M. Aron ◽  
Pablo Galindo
Keyword(s):  
Banach Space ◽  
Bilinear Form ◽  
Weakly Compact ◽  
Linear Forms ◽  
First Derivative ◽  
Multilinear Mappings ◽  
Arens Regularity

The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.

scholarly journals Regular multilinear operators on C(K) spaces

1999 ◽  
Vol 60 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Fernando Bombal ◽  
Ignacio Villanueva
Keyword(s):  
Banach Space ◽  
Holomorphic Mappings ◽  
Multilinear Operators ◽  
Arbitrary Banach Space ◽  
Multilinear Forms

The purpose of this paper is to characterise the class of regular continuous multilinear operators on a product of C(K) spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection with problems of factorisation of polynomials and holomorphic mappings. We also obtain several characterisations of a compact dispersed space K in terms of polynomials and multilinear forms defined on C(K).

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