Perturbation of a Fredholm complex by inessential operators.
Gleason, Jim (2001)
Georgian Mathematical Journal
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Gleason, Jim (2001)
Georgian Mathematical Journal
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M. Berkani, M. Sarih (2001)
Studia Mathematica
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Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only...
L. A. Coburn, A. Lebow (1966)
Rendiconti del Seminario Matematico della Università di Padova
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Valter Šeda (1983)
Annales Polonici Mathematici
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Recherche Coopérative sur Programme n°25
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Banach Center Publications
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We develop a difference equations analogue of recent results by F. Gesztesy, K. A. Makarov, and the second author relating the Evans function and Fredholm determinants of operators with semi-separable kernels.
David Ruelle (1989)
Recherche Coopérative sur Programme n°25
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Bogdan Bojarski, Giorgi Khimshiashvili (2005)
Open Mathematics
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We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold.