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Rank and the Drazin inverse in Banach algebras

R. M. Brits, L. Lindeboom, H. Raubenheimer (2006)

Studia Mathematica

Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.

Some inequalities involving upper bounds for some matrix operators. I

R. Lashkaripour, D. Foroutannia (2007)

Czechoslovak Mathematical Journal

In this paper we consider the problem of finding upper bounds of certain matrix operators such as Hausdorff, Nörlund matrix, weighted mean and summability on sequence spaces l p ( w ) and Lorentz sequence spaces d ( w , p ) , which was recently considered in [9] and [10] and similarly to [14] by Josip Pecaric, Ivan Peric and Rajko Roki. Also, this study is an extension of some works by G. Bennett on l p spaces, see [1] and [2].

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

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