Corrigendum and addendum:

J. Koliha; M. Mbekhta; V. Müller; Pak Poon

Displaying similar documents to “Corrigendum and addendum: 'On the axiomatic theory of spectrum II'”

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Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only...

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Let T be a bounded linear operator acting on a Banach space X. For each integer n, define $T_{n}$ to be the restriction of T to $R (T^{n})$ viewed as a map from $R (T^{n})$ into $R (T^{n})$ . In [1] and [2] we have characterized operators T such that for a given integer n, the operator $T_{n}$ is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where $T_{n}$ belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with...