On semi-Fredholm operators and the conjugate of a product of operators

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Perturbation Results on Semi-Fredholm Operators and Applications

We give some results concerning stability in the Fredholm operators and Browder operators set, via the concept of measure of noncompactness. Moreover, we prove some localization results on the essential spectra of bounded operators on Banach space. As application, we describe the essential spectra of weighted shift operators. Finally, we describe the spectra of polynomially compact operators, a...

Notes on Fredholm operators

(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...

Research Article Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

Some Remarks on Perturbation Classes of Semi-Fredholm and Fredholm Operators

We show the existence of Banach spaces X, Y such that the set of strictly singular operators ᏿(X,Y) (resp., the set of strictly cosingular operators Ꮿ᏿(X,Y)) would be strictly included in F + (X,Y) (resp., F − (X,Y)) for the nonempty class of closed densely defined upper semi-Fredholm operators Φ + (X,Y) (resp., for the nonempty class of closed densely defined lower semi-Fredholm operators Φ − ...