Fredholm properties of elliptic operators on Rn

A FREDHOLM THEORY FOR A CLASS OF FIRST-ORDER ELLIPTIC PARTIAL DIFFERENTIAL OPERATORS IN Rn

The objects of interest are linear first-order elliptic partial differential operators with domain //i(/?" ; C*) in L2(Rn;Ck), the first-order coefficients of which become constant and the zero-order coefficient of which vanishes outside a compact set in R". It is shown that operators of this type are "practically" Fredholm in the following way: Such an operator has a finite index which is inva...

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...

Fredholm Properties of Toeplitz Operators on Dirichlet Spaces

In this paper, the Fredholm properties of some Toeplitz operators on Dirichlet spaces be discussed, and the essential spectra of Toeplitz operators with symbols in C 1 or H ∞ 1 + C 1 be computed.

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...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators