The Glivenko-Cantelli Theorem in a Banach Space Setting

1992 ◽  
pp. 267-272
Author(s):  
Vladimir Dobrić
Keyword(s):  
Banach Space ◽  
Space Setting

scholarly journals TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

2010 ◽  
Vol 88 (2) ◽  
pp. 205-230 ◽  
Author(s):  
CHRISTOPH KRIEGLER ◽  
CHRISTIAN LE MERDY
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unconditional Basis ◽  
Compact Set ◽  
Bounded Operators ◽  
Space Setting ◽  
Uniformly Bounded

AbstractLet K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

scholarly journals Right and Left Weyl Operator Matrices in a Banach Space Setting

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Aichun Liu ◽  
Junjie Huang ◽  
Alatancang Chen
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Operator Matrix ◽  
Weyl Operator ◽  
Operator Matrices ◽  
Space Setting ◽  
Hamiltonian Operators ◽  
Equivalent Conditions

Let X i , Y i i = 1,2 be Banach spaces. The operator matrix of the form M C = A C 0 B acting between X 1 ⊕ X 2 and Y 1 ⊕ Y 2 is investigated. By using row and column operators, equivalent conditions are obtained for M C to be left Weyl, right Weyl, and Weyl for some C ∈ ℬ X 2 , Y 1 , respectively. Based on these results, some sufficient conditions are also presented. As applications, some discussions on Hamiltonian operators are given in the context of Hilbert spaces.

scholarly journals Quasi-regularity in Optimization

1986 ◽  
Vol 41 (2) ◽  
pp. 188-192 ◽  
Author(s):  
Kung-Fu Ng ◽  
David Yost
Keyword(s):  
Banach Space ◽  
Lagrange Multiplier ◽  
Optimization Problems ◽  
General Situation ◽  
Lagrange Multiplier Rule ◽  
Infinite Dimensional ◽  
Space Setting ◽  
Multiplier Rule ◽  
Dimensional Version ◽  
Definition Of

AbstractThe notion of quasi-regularity, defined for optimization problems in Rn, is extended to the Banach space setting. Examples are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.

scholarly journals Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2066
Author(s):  
Messaoud Bounkhel ◽  
Mostafa Bachar
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Space Setting ◽  
Nonlinear Anal ◽  
Finite Dimensional ◽  
In Trans ◽  
First Time ◽  
The Relationship ◽  
Primal Lower Nice Functions

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699–29].

scholarly journals The Jarratt method in Banach space setting

1994 ◽  
Vol 51 (1) ◽  
pp. 103-106 ◽  
Author(s):  
I.K. Argyros ◽  
Dong Chen ◽  
Qingshan Qian
Keyword(s):  
Banach Space ◽  
Space Setting ◽  
Jarratt Method

scholarly journals Regularity lemmas in a Banach space setting

2016 ◽  
Vol 51 ◽  
pp. 347-358
Author(s):  
Guus Regts
Keyword(s):  
Banach Space ◽  
Space Setting

scholarly journals A note on Fréchet and approximate subdifferentials of composite functions

1994 ◽  
Vol 49 (1) ◽  
pp. 111-115 ◽  
Author(s):  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Space ◽  
Simple Proof ◽  
Reflexive Banach Space ◽  
Composite Function ◽  
Composite Functions ◽  
Space Setting ◽  
Approximate Subdifferential

The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.

scholarly journals Data Dependence Results for Multistep and CR Iterative Schemes in the Class of Contractive-Like Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Vatan Karakaya ◽  
Faik Gürsoy ◽  
Kadri Doğan ◽  
Müzeyyen Ertürk
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Data Dependence ◽  
Iterative Schemes ◽  
Iterative Processes ◽  
Space Setting

We intend to establish some results on the data dependence of fixed points of certain contractive-like operators for the multistep and CR iterative processes in a Banach space setting. One of our results generalizes the corresponding results of Soltuz and Grosan (2008) and Chugh and Kumar (2011).

scholarly journals Regularity lemmas in a Banach space setting

2015 ◽  
Vol 49 ◽  
pp. 107-113
Author(s):  
Guus Regts
Keyword(s):  
Banach Space ◽  
Space Setting
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