H. Boua
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Essential Descent Spectrum Equality
Mbark Abkari, Hamid Boua, Abdelaziz Tajmouati
MFAT 30 (2024), no. 3-4, 101-104
101-104
A bounded operator $T$ in a Banach space $X$ is said to satisfy the essential descent spectrum equality, if the descent spectrum of $T$ coincides with the essential descent spectrum of $T$. In this note, we give some conditions under which the equality $\sigma_{desc}(T) = \sigma^e_{desc}(T)$ holds for $T$.
Equality between different types of invertibility
MFAT 27 (2021), no. 1, 31-36
31-36
Necessary and sufficient conditions for the between different types
of invertibility are established.
Встановлені необхідні та достатні умови співпадіння різних
типів оборотності.
Upper semi-Fredholm and Kato spectrum of an $\alpha$-times integrated semigroup
MFAT 26 (2020), no. 1, 63-67
63-67
Let $(T(t))_{t\geq 0}$ be an $\alpha$-times integrated semigroup with generator $A$ on a Banach space $X$. In this paper, we show that the spectral mapping theorem holds for upper semi-Fredholm spectrum and we will give some consequences of this result. We also give an application on the Schrödinger operator.
