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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
On B-Generalized Skew Derivations In Banach Algebras, Abdul Nadim Khan
On B-Generalized Skew Derivations In Banach Algebras, Abdul Nadim Khan
Turkish Journal of Mathematics
} Let $\mathscr{A}$ be a Banach algebra over $\mathbb{R}$ or $\mathbb{C}$. In this paper, we describe the behavior of recently defined $b$-generalized skew derivations which satisfy certain differential identities on some specific subsets of $\mathscr{A}$.
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Turkish Journal of Mathematics
Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.
Criteria Of Le Page Type In Involutive Banach Algebras, Abdellah El Kinani, Mohamed Oudadess
Criteria Of Le Page Type In Involutive Banach Algebras, Abdellah El Kinani, Mohamed Oudadess
Turkish Journal of Mathematics
The Le Page inequality in Banach algebras is \parallel xy \parallel\leq\alpha\parallel yx\parallel. We consider inequalities where a linear involution appears and has consequences on the involution itself and commutativity results.^1