The purpose of this paper is to introduce and study a new class operators that we call pseudogeneralized invertible operators. This includes both the generalized Drazin Some results connected with ascent essential are also obtained for class. relationship between pseudo-generalized operators, semi-Fredholm explored.

Abstract We define and study Toeplitz operators on the Fréchet space of all holomorphic functions finitely connected domains in Riemann sphere. completely characterize Fredholm, semi-Fredholm invertible belonging to this class. As a result, we obtain characterization these classes unit disk case. motivation formulate analyze Riemann–Hilbert problem which consider.

Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering type elements in a unital $$C^{*}$$ -algebra as generalization of -Fredholm operators on the standard Hilbert -module Mishchenko Fomenko properly infinite von Neumann algebra Breuer. In this paper, we establish semi-Fredholm -algebras continuation Lazović. We introduce notion element semi-Weyl -algebra. prove ...

Continuing a line of investigation initiated in [11] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman–Schwinger type integral operators, we here examine the stability index, or sign of the first nonvanishing derivative at frequency zero of the characteristic determinant, an object that has found considerable use in the study by Evans func...

We introduce a new concept of perturbation of closed linear subspaces and operators in Banach spaces called uniform λ−adjustment which is weaker than perturbations by small gap, operator norm, q−norm, and K2−approximation. In arbitrary Banach spaces some of the classical Fredholm stability theorems remain true under uniform λ−adjustment, while other fail. However, uniformly λ−adjusted subspaces...

Let (U(t))t≥0 be a C0-semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semiFredholm) operator, then (U(t))t≥0 is a Fredholm (resp., semi-Fredholm) semigroup. Moreover, we give a necessary and sufficient condition guaranteeing that (U(t))t≥0 can be embedded in a C0-group on X. Also we study semigroups whi...

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals. Let H be a complex infinite-dimensional separable Hilbert space, which is of course unique up to isomorphism. Let B(H) be the Banach algebra of bounded linear operators on H, and let C(H) be the clo...

Abstract Let $${{\mathcal {S}}}{{\mathcal {S}}}$$ S and {C}}}$$ C be the strictly singular cosingular operators acting between Banach spaces, let $$P\Phi _+$$ P Φ + perturbation classes for upper ...