Spectral properties of generalized inverses

• Autorzy: Schmoeger Ch.
• Języki publikacji: EN

Abstrakty

EN

Let A denote a unital complex Banach algebra. An element a € A is said to be relatively regular if aba = a for some b 6 A. Then b will be called a generalized inverse of a. In this note we study spectral properties of generalized inverses of a.

Słowa kluczowe

EN

Banach algebra; generalized inverse; relative regularity

PL

algebra Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 1
• Strony: 137--148
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Schmoeger Ch.

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

Bibliografia

• [1] F.F. Bonsall, J. Duncan, Complete Normed Algebras, Springer, Berlin-Heidelberg-New York, 1973.
• [2] S.R. Caradus, Generalized Inverses and Operator Theory. Queen's papers in pure and applied mathematics, No. 38, Queen's University, Kingston, Ontario, 1974.
• [3] R. Harte, Invertibility and Singularity for Dounded Linear Operators, Marcel Dekker, New York-Basel, 1988.
• [4] R. Harte, M. Mbekhta, On generalized inverses in C*-algebras, Studia Math. 103 (1992), 71-77.
• [5] H. Heuser, Funktionalanalysis, 3. ed. Teubner, Stuttgart, 1991.
• [6] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413.
• [7] V. Rakocevic, Moore-Penrose inverse in Banach algebras, Proc. R. Ir. Acad., Sect. A, 88 (1988), 57-60.
• [8] Ch. Schmoeger, On a class of generalized Fredholm operators, II, Demonstratio Math. 31 (1998). 705-722.
• [9] Ch. Schmoeger, The punctured neighbourhood theorem in Banach space algebras, Proc. R. Ir. Acad. Sect. A, 91 (1991), 205-218.