scholarly journals On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility

2013 ◽  
Vol 173 (3) ◽  
pp. 379-415 ◽  
Author(s):  
Daniel Pellegrino ◽  
Joilson Ribeiro
Keyword(s):  
Banach Spaces ◽  
New Approach ◽  
Polynomial Ideals

scholarly journals Holomorphic functions and polynomial ideals on Banach spaces

2010 ◽  
Vol 63 (1) ◽  
pp. 71-91 ◽  
Author(s):  
Daniel Carando ◽  
Verónica Dimant ◽  
Santiago Muro
Keyword(s):  
Banach Spaces ◽  
Holomorphic Functions ◽  
Polynomial Ideals

scholarly journals Nonlinear sequential fractional differential equations in partially ordered spaces

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4577-4586 ◽  
Author(s):  
Hossein Fazli ◽  
Juan Nieto
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
New Approach ◽  
Partially Ordered ◽  
Fractional Differential ◽  
Partially Ordered Spaces ◽  
Sequential Fractional Differential Equations ◽  
Ordered Banach Spaces

In this paper, some new partially ordered Banach spaces are introduced. Based on those new partially ordered Banach spaces and applying some fixed point theorems, we present a new approach to the theory of nonlinear sequential fractional differential equations. An example illustrating our approach is also discussed.

A new approach to measures of noncompactness of Banach spaces

2018 ◽  
Vol 240 (1) ◽  
pp. 21-45 ◽  
Author(s):  
Lixin Cheng ◽  
Qingjin Cheng ◽  
Qinrui Shen ◽  
Kun Tu ◽  
Wen Zhang
Keyword(s):  
Banach Spaces ◽  
Measures Of Noncompactness ◽  
New Approach

scholarly journals Homogeneous operators and essential complexes

1989 ◽  
Vol 31 (1) ◽  
pp. 73-85 ◽  
Author(s):  
F.-H. Vasilescu
Keyword(s):  
Banach Spaces ◽  
Small Perturbations ◽  
New Approach ◽  
Non Linear ◽  
Homogeneous Mappings ◽  
The Stability ◽  
Homogeneous Operators ◽  
Fredholm Complexes ◽  
Gap Topology

The aim of this work is to present a new approach to the concept of essential Fredholm complex of Banach spaces ([10], [2]; see also [11], [4], [6], [7] etc. for further connections), by using non-linear homogeneous mappings. We obtain some generalized homotopic properties of the class of essential Fredholm complexes, in our sense, which are then applied to establish its relationship with similar concepts. We also prove the stability of this class under small perturbations with respect to the gap topology.

scholarly journals Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2510
Author(s):  
Deepak Kumar ◽  
Sunil Kumar ◽  
Janak Raj Sharma ◽  
Lorentz Jantschi
Keyword(s):  
Convergence Analysis ◽  
Banach Spaces ◽  
Complex Geometry ◽  
Basins Of Attraction ◽  
New Approach ◽  
Convergence Error ◽  
Uniqueness Of The Solution ◽  
Dynamical Nature ◽  
Fifth Order ◽  
Local Convergence Analysis

We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, error bounds on the distances involved, and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples are provided to validate the theoretical results. Convergence domains of the methods are also checked through complex geometry shown by drawing basins of attraction. The boundaries of the basins show fractal-like shapes through which the basins are symmetric.

scholarly journals Coherent sequences of polynomial ideals on Banach spaces

2009 ◽  
Vol 282 (8) ◽  
pp. 1111-1133 ◽  
Author(s):  
Daniel Carando ◽  
Verónica Dimant ◽  
Santiago Muro
Keyword(s):  
Banach Spaces ◽  
Polynomial Ideals

A New Approach to Operator Spaces

1991 ◽  
Vol 34 (3) ◽  
pp. 329-337 ◽  
Author(s):  
Edward G. Effros ◽  
Zhong-Jin Ruan
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Operator Space ◽  
Operator Spaces ◽  
New Approach ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Space Concepts ◽  
Injective Operator

AbstractThe authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.

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