scholarly journals On the concept of orientability for Fredholm maps between real Banach manifolds

2000 ◽  
Vol 16 (2) ◽  
pp. 279 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Massimo Furi
Keyword(s):  
Banach Manifolds ◽  
Fredholm Maps

On the product formula for the oriented degree for Fredholm maps of index zero between Banach manifolds

2002 ◽  
Vol 48 (6) ◽  
pp. 853-867 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Product Formula ◽  
Index Zero ◽  
Banach Manifolds ◽  
Fredholm Maps

scholarly journals Global Persistence of the Unit Eigenvectors of Perturbed Eigenvalue Problems in Hilbert Spaces: The Odd Multiplicity Case

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 561
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Hilbert Spaces ◽  
Eigenvalue Problems ◽  
Eigenvalues And Eigenvectors ◽  
Index Zero ◽  
Global Continuation ◽  
Banach Manifolds ◽  
Unperturbed Problem ◽  
Fredholm Maps

We study the persistence of eigenvalues and eigenvectors of perturbed eigenvalue problems in Hilbert spaces. We assume that the unperturbed problem has a nontrivial kernel of odd dimension and we prove a Rabinowitz-type global continuation result. The approach is topological, based on a notion of degree for oriented Fredholm maps of index zero between real differentiable Banach manifolds.

Linear Operators in Banach Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Fredholm Maps

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to derive important results later in the book.

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

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