A note on the index of $B$-Fredholm operators

M. Berkani; Dagmar Medková

Displaying similar documents to “A note on the index of $B$ -Fredholm operators”

Ascent, descent and roots of Fredholm operators

Bertram Yood (2003)

Studia Mathematica

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Let T be a Fredholm operator on a Banach space. Say T is rootless if there is no bounded linear operator S and no positive integer m ≥ 2 such that $S^{m} = T$ . Criteria and examples of rootlessness are given. This leads to a study of ascent and descent whether finite or infinite for T with examples having infinite ascent and descent.

A Note on the Alexander Theorem on the Complex Plane

Sylwester Zając (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate the Banach manifold consisting of complex $^{r}$ functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.

Extended Weyl type theorems

M. Berkani, H. Zariouh (2009)

Mathematica Bohemica

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An operator $T$ acting on a Banach space $X$ possesses property $(gw)$ if $σ_{a} (T) ∖ σ_{{SBF}_{+}^{-}} (T) = E (T),$ where $σ_{a} (T)$ is the approximate point spectrum of $T$ , $σ_{{SBF}_{+}^{-}} (T)$ is the essential semi-B-Fredholm spectrum of $T$ and $E (T)$ is the set of all isolated eigenvalues of $T .$ In this paper we introduce and study two new properties $(b)$ and $(gb)$ in connection with Weyl type theorems, which are analogous respectively to Browder’s theorem and generalized Browder’s theorem. Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space...

B-Fredholm and Drazin invertible operators through localized SVEP

M. Amouch, H. Zguitti (2011)

Mathematica Bohemica

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Let $X$ be a Banach space and $T$ be a bounded linear operator on $X$ . We denote by $S (T)$ the set of all complex $λ \in ℂ$ such that $T$ does not have the single-valued extension property at $λ$ . In this note we prove equality up to $S (T)$ between the left Drazin spectrum, the upper semi-B-Fredholm spectrum and the semi-essential approximate point spectrum. As applications, we investigate generalized Weyl’s theorem for operator matrices and multiplier operators.

On a Fučík problem

Valter Šeda (1983)

Annales Polonici Mathematici

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Restriction of an operator to the range of its powers

M. Berkani (2000)

Studia Mathematica

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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...