Fredholm Theory

Generalized Kato-Riesz decomposition and generalized Drazin-Riesz invertible operators

“…Then there exists (M, N ) ∈ Red(A) such that A M is Saphar and A N is Riesz. Further we conclude that A M has the SVEP at 0 and according [1,Theorem 2.49] it follows that A M is left invertible.…”

“…From the proof of [1,Theorem 1.43] it follows that A ′ N ⊥ is Kato. Therefore, A ′ N ⊥ is Saphar, and so A ′ admits a GSRD(N ⊥ , M ⊥ ).…”

The perturbation classes problem for subprojective and superprojective Banach spaces

“…We begin with a simple result that can be found in [1,Theorem 7.21]. We include a proof for the convenience of the reader.…”

Property (Bv) and Tensor Product

“…In addition, we denote by p(T) and q(T) the ascent and descent of T, respectively. See [1] for more details. Some spectra mentioned above have been generalized by ).…”