On a class of generalized Fredholm operators, VI

• Autorzy: Schmoeger C.
• Języki publikacji: EN

Abstrakty

EN

Let X be a complex Banach space and T a generalized Fredholm operator on X (see [3] , [4] , [5] , [6] and [7] ). In [7] we have shown that T has a Kato decomposition (Xl, X2). We say that a Kato decomposition (Xl, X2) of T is non-trivial if X2= {0}. The main result of this paper reads as follows: Let T be a generalized Fredholm operator with a non-trivial Kato decomposition. Then (i) The subspace X2 of each Kato decomposition of T is unique if and only if T has finite ascent. (ii) The subspace Xl of each Kato decomposition of T is unique if and only if T has finite descent. (iii) T has a unique Kato decomposition if and only if 0 is a pole of the resolvent (T - lambaI)-l.

Słowa kluczowe

EN

generalized Fredholm operators; Banach space

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 1999
• Tom: Vol. 32, nr 4
• Strony: 811--822
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Schmoeger C.

• Mathematisches Institut I Universitat Karlsruhe D-76128 Karlsruhe, Germany,