EUDML

Let $B (X)$ be the algebra of all bounded linear operators in a complex Banach space $X$ . We consider operators $T_{1}, T_{2} \in B (X)$ satisfying the relation $σ_{T_{1}} (x) = σ_{T_{2}} (x)$ for any vector $x \in X$ , where $σ_{T} (x)$ denotes the local spectrum of $T \in B (X)$ at the point $x \in X$ . We say then that $T_{1}$ and $T_{2}$ have the same local spectra. We prove that then, under some conditions, $T_{1} - T_{2}$ is a quasinilpotent operator, that is $∥ {(T_{1} - T_{2})}^{n} ∥^{1 / n} \to 0$ as $n \to \infty$ . Without these conditions, we describe the operators with the same local spectra only in some particular cases.

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Finiteness of spectra of graphs obtained by some operations on infinite graphs.

On the automorphism group of an infinite graph.

Sous-groupes distingues du groupe unitaire et du groupe général linéaire d'un espace de Hilbert quaternionien.

A property of canonical graphs.

On the numbers of positive and negative eigenvalues of a graph.

Representation theorems for sequences of the classes $C R_{c}$ and $E R_{c}$ .

A theorem of Galambos-Bojanić-Seneta type.

The strong asymptotic equivalence and the generalized inverse.

On The Symmetric Quaternionic Banach Algebras, I (Geljfand Theory)

The Spectrum Of Line Graphs Of Some Infinite Graphs

On operators with the same local spectra

Graphs whose energy does not exceed 3

On Spectra of Infinite Graphs

Graphs with the Reduced Spectrum in the Unit Interval

Maximal Canonical Graphs with Three Negative Eigenvalues