scholarly journals AN ELEMENTARY PROOF OF JAMES’ CHARACTERIZATION OF WEAK COMPACTNESS

2011 ◽  
Vol 84 (1) ◽  
pp. 98-102 ◽  
Author(s):  
WARREN B. MOORS
Keyword(s):  
Integral Representation ◽  
Banach Spaces ◽  
Elementary Proof ◽  
Weak Compactness ◽  
Representation Theorems

AbstractIn this paper we provide an elementary proof of James’ characterization of weak compactness in separable Banach spaces. The proof of the theorem does not rely upon either Simons’ inequality or any integral representation theorems. In fact the proof only requires the Krein–Milman theorem, Milman’s theorem and the Bishop–Phelps theorem.

scholarly journals On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1061-1068
Author(s):  
Seda Öztürk
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Integral Representation ◽  
Unit Circle ◽  
Banach Spaces ◽  
Fourier Coefficients ◽  
Linear Representation ◽  
Complex Banach Space ◽  
Continuous Linear

In this paper, for an isometric strongly continuous linear representation denoted by ? of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A?r (x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A?r and ?.

AN ELEMENTARY PROOF OF JAMES’ CHARACTERISATION OF WEAK COMPACTNESS. II

2016 ◽  
Vol 95 (1) ◽  
pp. 133-137 ◽  
Author(s):  
WARREN B. MOORS ◽  
SAMUEL J. WHITE
Keyword(s):  
Banach Spaces ◽  
Elementary Proof ◽  
Weak Compactness

In this paper we provide an elementary proof of James’ characterisation of weak compactness for Banach spaces whose dual ball is weak∗sequentially compact.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals A Functional Characterization of Almost Greedy and Partially Greedy Bases in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1827
Author(s):  
Pablo Manuel Berná ◽  
Diego Mondéjar
Keyword(s):  
Banach Spaces ◽  
Functional Characterization

In 2003, S. J. Dilworth, N. J. Kalton, D. Kutzarova and V. N. Temlyakov introduced the notion of almost greedy (respectively partially greedy) bases. These bases were characterized in terms of quasi-greediness and democracy (respectively conservativeness). In this paper, we show a new functional characterization of these type of bases in general Banach spaces following the spirit of the characterization of greediness proved in 2017 by P. M. Berná and Ó. Blasco.

scholarly journals Sets of periods for chaotic linear operators

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. A. Conejero ◽  
F. Martínez-Giménez ◽  
A. Peris ◽  
F. Rodenas
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Linear Operators

AbstractWe provide a complete characterization of the possible sets of periods for Devaney chaotic linear operators on Hilbert spaces. As a consequence, we also derive this characterization for linearizable maps on Banach spaces.

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

scholarly journals Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

Positivity ◽  
2012 ◽  
Vol 17 (3) ◽  
pp. 535-587
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Banach Spaces ◽  
Bmo Functions ◽  
Umd Banach Spaces
Sign in / Sign up

Export Citation Format

Share Document