We extend the recent stability results of Ambrozie for Fredholm essential complexes to the semi-Fredholm case. Let X,Y be Banach spaces. By an operator we always mean a bounded linear operator. The set of all operators from X to Y will be denoted by L(X,Y ). Denote by N(T ) and R(T ) the kernel and range of an operator T ∈ L(X, Y ). Recall that an operator T : X → Y is called semi-Fredholm if i...

Let A be a bounded operator on a separable, infinite dimensional Hilbert space H. Moreover, assume that A is not in the set C + K(H) of operators expressible as a sum of a scalar multiple of identity and a compact operator. What is the smallest similarity invariant semigroup containing operator A? Equivalently, which operators can be expressed as products of operators, similar to A? A partial a...

A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator matrix (

This paper is concerned with the influence of frequency modulation on the semiFredholm properties of Toeplitz operators with oscillating matrix symbols. The main results give conditions on an orientation-preserving homeomorphism α of the real line that ensure the following: if b belongs to a certain class of oscillating matrix functions (periodic, almost periodic, or semi-almost periodic matrix...

Let 7(S) denote the reduced minimum modulus of a linear operator S acting in a complex Banach space X, and let / denote the identity on X. In this paper it is shown that for a (not necessarily bounded) Fredholm operator T acting in X, the limit lim y^fy/rt exists and is equal to the supremum of all positive numbers S such that the dimension of the null space and the codimension of the range of ...

The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish...

This paper is concerned with the study of a class of closed linear operators densely defined on a Hilbert space H and called B-Fredholm operators. We characterize a B-Fredholm operator as the direct sum of a Fredholm closed operator and a bounded nilpotent operator. The notion of an index of a B-Fredholm operator is introduced and a characterization of B-Fredholm operators with index 0 is given...